The Lottery Fallacy, Fine-Tuning, and the Multiverse

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Our best current science suggests that our universe is fine-tuned for life. That is to say, certain numbers in basic physics – e.g. the strength of gravity, the mass of electrons, etc. – are, against improbable odds, exactly as they need to be for life to be possible. Many scientists and philosophers think this is evidence for a multiverse, but I disagree. What we have evidence for us that our universe is fine-tuned and postulating a huge number of other universes doesn’t explain this.

I recently wrote a Scientific American article on this, and there have been two blog posts from Skeptics Guide to the Universe in response. Earlier this week, host Steve Novella and I got together to discuss the issue, and an edited version of our discussion will be going up on their podcast tomorrow. The discussion prompted me to clarify my argument in my own mind, and I’d like to share here how I’m thinking about it now.

Steve accuses me of committing the lottery fallacy. But what is the lottery fallacy? Suppose against improbable odds my lottery numbers come up. Clearly there’s something going wrong if I think there needs to be some special explanation of the fact that I won. Steve suggests that the error consists in focusing on the particular person who won – Philip Goff – rather than merely the fact that someone won. Similarly, by focusing on the fact that our universe – rather than just some universe – is fine-tuned, he thinks I’m committing the same fallacy.

I don’t think this is the right explanation of the lottery fallacy. Sometimes a focus on the particular person is appropriate. Suppose, for example, that the partner of the person who picked the numbers wins on a billion to one odds. Then it does seem we want to focus on the particular person who won.

What’s the difference between the two cases? The fact that Philip Goff won the lottery is improbable, but it’s not improbable that it happened by chance. Why is that? Because there’s no (non-ad hoc) non-chance hypothesis that would render it much more probable. Whereas when it comes to the fact that the partner of the person who picked the numbers won, this is just as improbable as Philip Goff winning, but in this case it’s not only improbable but improbable that it happened by chance. Why? Because there is a (non-ad hoc) non-chance hypothesis that would render it more probable, namely the hypothesis that there was collusion between the person who chose the numbers and her partner. Assuming that hypothesis, it’s much more likely that the partner would win that it is on the hypothesis that the numbers were picked randomly.

What about the fine-tuning case? I think we’re struck by the fine-tuning not because it’s improbable – whatever numbers had come up would be equally improbable – but because it’s improbable that it happened by chance. And, again, this is because there’s a non-chance hypothesis that would render it much more probable, namely the hypothesis that considerations of value were involved in determining the values of the constants. If the process that determined the constants was sensitive to the value of the resulting universe, then it wouldn’t be surprising that the constants would end up fine-tuned, much less surprising that it would be if they were selected at random.

So I don’t think the lottery fallacy is anything to do with focusing on the particular individual rather than the general fact; rather it’s a matter of fallaciously inferring from the fact that something is improbable to the fact it’s improbable that it happened by chance. But the fact that our universe in fine-tuned is not only improbable, it’s also improbable that it happened by chance. Therefore, focusing on the fact that our universe is fine-tuned – rather than that some universe is fine-tuned – does not commit the lottery fallacy.

So that’s why I don’t agree with Steve’s argument against my position. Let me try a different way of making the case for my position (this is a modified form of the argument White defends in the postscript to a reprint of this article). We can only gain support for a hypothesis with the evidence we in fact have. We can either think of evidence as our actual observations, or as the concrete, physical states of affairs we know about through observation. Whether you think of the fine-tuning evidence as our actual observations, or you think of it as the concrete fine-tuned physical universe we live in, in either case our evidence is not made more probable by the multiverse hypothesis. Yes, the existence of some fine-tuned universe is made more probable by that hypothesis. But we have to work with the evidence we in fact have, and the evidence we in fact have is constituted by the properties of this concrete, physical universe (or our observations of it), and this is not made more probable by the multiverse hypothesis

Many people have worried about the Joker analogy I make in my Scientific American article, on the grounds that, in this thought experiment, you pre-exist the flukey event. In the discussion I had with Steve, I got around this with a different thought experiment. Suppose your conception came about through IVF. And suppose you discover as an adult that when the doctor fertilised the egg, she rolled twenty dice to see whether she’d do it, committing only to fertilise the egg if they all came up sixes. Does your discovery that your birth was dependent on this improbable event provide you with evidence that the doctor did the same in many other IVF cases, rolling dice to decide whether to fertilise the egg? I don’t think so; all you have evidence for is that your conception was decided in this way, and whether or not the doctor did this in other cases has no bearing on how likely it was that the right numbers would come up with your conception. By analogy, all we have evidence for is that the right numbers came up for our universe, and whether or not there are other universes has no bearing on how likely it was that the right numbers came up for our universe.

In correspondence after our discussion, Steve proposed tweaking the thought experiment: suppose I’m considering whether the doctor rolled dice many times or only once to decide whether to fertilise the egg that made me. I agree in that case you would have evidence for that hypothesis, as that hypothesis makes *your* existence more likely, and your existence constitutes your evidence. But that modified IVF hypothesis corresponds to a sci fi scenario in which our universe had a number of shots at fixing its constants (i.e. random processes reset them numerous times) and the Guardian of the Universe only allowed it to proceed if they came up fine-tuned. That hypothesis would make our evidence (our fine-tuned universe) more likely. But that’s not the multiverse hypothesis. According to the standard multiverse hypothesis (eternal inflation + string theory) our universe had only one shot at fixing its constants. That corresponds to a scenario in which there is only one dice roll to determine whether the egg that produced you gets fertilised.  

In our discussion, Steve came up with another thought experiment. Suppose the mischievous god Loki has just brought you into existence, and he tells you that he rolled twenty dice to decide whether or not to create a person, committing only to create a person if they all came up six (I’ve modified the example a little to make it similar to mine, but the substance is the same). Do you have grounds to think Loki has done this many times, on the assumption that each time he creates a person it’s a distinct person? I admit I did have to think about this one, and my intuitions are less firm that in the IVF case. So we need an explanation of why intuitions are different in these two cases. I suggest it’s because in the IVF case, it’s totally clear that the hypothesis I’m considering is one in which other babies would be born who aren’t me, whereas in the Loki case, it’s easy to slip into thinking he’s been having lots of shots at creating me. If I’m considering the scenario in which Locki had numerous shots at creating me, then I do find evidential support. But this is analogous to the tweaked IVF thought experiment in which the doctor rolled dice numerous times to decide whether to create me, and, as I argued above, this does not mirror the real-world fine-tuning case.

In summary: the fine-tuning is very puzzling, but it’s not evidence that we live in a multiverse.

The Author

I am a philosopher and consciousness researcher at Durham University, UK. My research focuses on how to integrate consciousness into our scientific worldview.

295 Comments

  1. Hi Dmitriy,

    Thanks for pointing out the precise points of disagreement for me.

    Does PM(N, p1) just mean P(M | p = p1)? I’m mostly asking about what PM means, but also I didn’t need to use N in my argument, so I don’t think it really matters. You may think it’s additional evidence we should use, but I don’t see how it would change anything if we did, especially as we don’t know what N actually is.

    In any case I accept your point A. It is clearer to translate “Does fine tuning give us reason to increase our credence in M” by thinking of it as that a change in p should reflect a change in credence (lower p leading to greater credence). But I wouldn’t say this is an important problem. It’s not too hard to adapt the argument to this way of thinking of it. My original argument is equivalent to starting with p of 1 (absolutely no fine tuning — all possible worlds supporting observers) and changing to p of 10^(-9). So I accept (and appreciate) this as a helpful nitpick rather than a serious issue. I can redo the argument with this in mind if you think it would help.

    Point B is more interesting, but also not very surprising, as it seems to be more or less the objection I anticipated. I’m not really seeing anything there that is not entailed by my E1, so I don’t see any point in distinguishing your evidence from that.

    It seems to be a technical point whether or not some evidence Ex gives us reason to increase our credence in some hypothesis H if P(H|Ex) > P(H) but we also have evidence Ey and P(H|Ex&Ey) = P(H). I think you could argue it either way. In any case I would agree that we should use all the evidence available to us, so it would be fallacious to reason from Ex alone if we also have Ey. If Ex is O and Ey is E1 (using the terminology from my writeup), then it’s academic as we can’t but be sure of both.

    But we could imagine that there is some omniscient God’s eye view where O and E1 are equivalent because this universe is really just some universe from that perspective. If you wanted to argue that from the God’s eye view, E1 (that this particular universe is fine-tuned and actual) is more evidence than O and should change our analysis, I think you would be clearly wrong. Because if knowing that some winning lottery ticket was sold causes you to increase your estimate of the number of tickets sold (and it does), then knowing which specific ticket won should not change anything (and it shouldn’t). We can discuss that if you do in fact want to make such a claim.

    What I think you want to say is that from our perspective, where this particular universe is special to us, E1 changes our analysis. If we win the lottery ticket ourselves, then we have no reason to increase our estimate of how many lottery tickets were sold. I agree with this in the case of the lottery, but not in the case of fine tuning, because the universe was not special to us at the time its constants were decided (because we did not exist). This universe’s specialness to us is indeed contingent on its being fine-tuned in the first place, unlike the lottery ticket which would have been ours even if it hadn’t won. As such I think it’s more like the case where we learn that some lottery ticket has won — it is only brought to our attention at all because it is the winning ticket and not because it was ours. In the case of fine-tuning, I would say the universe is ours in part because it is fine tuned.

    So, after all of this argument, we’re back to exactly where we started with Philip Goff’s arguments. The issue is entirely down to which perspective we should take — the God’s eye perspective or the perspective where this universe is special to us because it’s ours. This issue is entirely decided by how we ought to think of personal identity.

    The one remaining wrinkle for me is how you reconcile your two conflicting positions.

    Copying and pasting myself from earlier in case you missed it:

    One position you advance seems to suggest that the fact that your experience exists gives you reason to raise your credence in M. Another position you advance seems to suggest the opposite.

    The former is “I know my total experience has been actualized in reality, since I am the one experiencing it. It is N times more likely to have been actualized if there are N universes instead of one (assuming it was very unlikely even on M).”

    The latter is that your own fine-tuning argument shows that the existence of a Dmitriy gives you no reason to increase your credence of M, because “it makes no difference whether p refers to fine-tuning or the chance of making a Dmitriy”

    Neither of these positions really accords with mine, both because you’re not that special (no offense). So I don’t think your existence gives you reason to increase your credence in M (rejecting position 1), and I do think it makes a difference whether p refers to fine-tuning or making a Dmitriy, because the former is remarkable and needs an explanation and the latter is not and can be attributed to chance alone.

    I still think your ensemble argument is flat out wrong, identity questions notwithstanding. I don’t see how this identity issue has any bearing on it. There’s nowhere in your ensemble argument where you make use of the fact that this specific universe is fine tuned. You’re only talking about populations of unidentified universes. As such, the fact that you reach the same conclusion as Philip Goff is entirely coincidental as far as I can see. Worse, your ensemble argument is obfuscatory (not accusing you of doing this deliberately, by the way). It seems to show with a pretty straightforward mathematical analysis that fine tuning has no bearing on P(M), but if the conclusion is right it has nothing to do with the reasons explored in the analysis. Your assumptions about identity and the evidence we have — given our unique perspective — are not made clear on your blog. The ensemble analysis would therefore appear to be wrong even if your criticism B of my Bayesian analysis is right.

    The problem again with your analysis is that you’re giving an arbitrary predetermined credence weighting to M vs S which remains unchanged before and after considering fine-tuning, when the assumption of most scientists is that fine-tuning should cause us to increase our credence in M. The argument on your blog post is able to prove this assumption wrong only by assuming it is wrong, so the argument is circular. If taking E1 into account truly does undermine the Bayesian analysis, then that’s the beginning and the end of the argument. It might make your ensemble argument valid, but only because it explains why you should not update your model to reflect your updated credences (just because there is no reason to update your credences in the first place, not because it would be double-dipping to do so). The ensemble argument is a neat attempt to get around these difficult identity/perspective issues but it fails by taking a position on them and in particular by doing so implicitly, and so never actually addressing the core issues.

    • Alex Popescu says

      Hey DM,

      I don’t want to get into these conversations once again. But I would like to quickly reiterate RMT’s point regarding what you wrote here:

      “The problem again with your analysis is that you’re giving an arbitrary predetermined credence weighting to M vs S which remains unchanged before and after considering fine-tuning, when the assumption of most scientists is that fine-tuning should cause us to increase our credence in M. The argument on your blog post is able to prove this assumption wrong only by assuming it is wrong, so the argument is circular.”

      As RMT said; to say that fine tuning should modify our credence in M, IS to say that the odds ratio between M and S should change on account of fine tuning. The meanings are equivalent. To say that we update our credences; is just to say the odds ratios have changed in the way shown.

      Also, I dispute your claim that most scientists have agreed that fine tuning should modify our credences in such a way; that is very much in contention. However, ultimately your claim that we are begging the question makes no sense. We can’t be, as you put it, saying that fine tuning makes no difference because we’ve assumed it makes no difference. We made no such assumptions in our analysis; notice that the ensemble does not stipulate anywhere that P must not modify the odds ratio. Rather, this is the conclusion; the very thing being demonstrated.

      It makes no sense to say that we can’t have demonstrated this because we must still nevertheless update our credences on the basis of P. That’s like saying that we can’t have demonstrated A, because A has to be the case. It is you who are begging the question here, not RMT. Granted, you invoked authority (most scientists think that…), but that is a very weak assertion.

      So RMT, by showing that the odds ratio don’t change, is demonstrating that we shouldn’t update our credence for M on the basis of P; because the two are literally saying the exact same thing.

    • Alex Popescu says

      Also this:
      “I know my total experience has been actualized in reality, since I am the one experiencing it. It is N times more likely to have been actualized if there are N universes instead of one (assuming it was very unlikely even on M).”

      Is not, as you contend, incompatible with this:
      “ Dmitriy gives you no reason to increase your credence of M, because “it makes no difference whether p refers to fine-tuning or the chance of making a Dmitriy”

      The first demonstrates that we update our credences on the basis of N; the second that we don’t do so on the basis of P (or the existence of Dmitriy). Both statements are fully compatible; I think you’re confused here with all due respect.

  2. Hi Alex,

    Thanks for addressing these points. I would say for most of this that you should understand by now where I’m coming from — that what I’m saying makes sense given my assumptions and so you need to tackle those assumptions rather than denying my statements. These assumptions now all rest on the Bayesian argument. If you don’t tackle that then nothing else will follow.

    > to say that fine tuning should modify our credence in M, IS to say that the odds ratio between M and S should change on account of fine tuning.

    And they would, if you updated your model as you should, after updating your credence as you should following the Bayesian argument. All possibilities are not equal. You need to weight M and S according to their credences.

    > Also, I dispute your claim that most scientists have agreed that fine tuning should modify our credences in such a way; that is very much in contention.

    I shouldn’t have said “most scientists”, agreed. Most scientists have offered no opinion on this at all, especially those who are not cosmologists or physicists. I wouldn’t say it’s contentious though. What is contentious is whether a multiverse is a good explanation in the first place. Lots of scientists think it isn’t because it isn’t falsifiable, or because it’s self-defeating, discouraging us from finding a deeper explanation. I’m not aware of any cosmologists or physicists (other than Dmitriy) who have explicitly said that the inference is logically unsound — although I’m sure there are some. But anyway, that hardly matters very much either way. This isn’t really an argument from authority. It’s just establishing that this is the default, intuitive assumption which you’re trying to disprove. I would say the burden of proof is on you (but that also doesn’t matter very much either way). This point can be ignored if you like as nothing very serious rests on it.

    > We can’t be, as you put it, saying that fine tuning makes no difference because we’ve assumed it makes no difference. We made no such assumptions in our analysis

    By not updating the credences/weights in your ensemble model, you assumed that it made no difference. I agree that you did not explicitly assume it, and you are not aware that you are assuming it, but by designing the ensemble model as you did, I claim that you assumed it implicitly and mistakenly.

    > It makes no sense to say that we can’t have demonstrated this because we must still nevertheless update our credences on the basis of P.

    You must update your credences on the basis of P because of the Bayesian argument. Only then will you get the right answer from the ensemble argument.

    > The first demonstrates that we update our credences on the basis of N; the second that we don’t do so on the basis of P (or the existence of Dmitriy). Both statements are fully compatible; I think you’re confused here with all due respect.

    If so, I’m still just as confused. In Dmitriy’s statement, N is the number of actual universes and N is unknown. The hypothesis that N is big is just M. N is therefore not evidence that we use to update our credence. Rather we have credence in the value of N. Dmitriy seems to me to be saying that as the likeliness of his existence is proportional to N, the fact that he exists gives reason to believe M (especially if he is unlikely to exist if N=1). I agree with your interpretation of the second statement, which is that he doesn’t update his credence in M on the fact that he exists.

    • Also Alex, note that as I’ve added a fuller Bayesian argument leading precisely to the conclusion I’m trying to prove, I don’t think you can say any longer that the Bayesian argument and the ensemble argument can both be correct but proving different things.

      It’s fine if you want to leave it to RMT to debate the Bayesian argument, but as everything follows from this the other points are not worth arguing. Take my above post as making claims iff my Bayesian argument holds. If there’s a problem with the Bayseian argument, then none of that follows.

      • Well some of it still holds. If the only problem with the Bayesian argument relates to the points about taking in the full evidence in light of our perspective as observers in this specific universe, then I would stand by my points saying that the ensemble argument is obfuscatory because it doesn’t make use of this evidence or make its importance clear, and gets to the right answer only by happenstance.

    • Alex Popescu says

      It wasn’t my intention to get into the Bayesian analysis; just to clarify some points. I think this clarification is still vital, and I think you are still misunderstanding some issues. First of all, I don’t agree that your points make sense if you are correct.

      Even if it’s true that fine tuning modifies the credence and odds ratio, it doesn’t follow that RMT or I are begging the question. Your point about the burden of proof is completely irrelevant. We are accepting the burden, and then going on to show that fine tuning makes no difference (we argue).

      So whether we should take your Bayesian analysis into account has no bearing on whether the ensemble is invalid as you claim. At best, if you are correct, then the assumptions of the analysis are incorrect (it is unsound). It doesn’t follow from that that RMT makes an implicit assumption, as you claim, that fine tuning makes no difference. He may of course be making an incorrect assumption (i.e. that it is the ratio of observers that matters as opposed to the existence of a single observer).

      So it doesn’t follow from “I have an argument that defeats RMT’s points” that “RMT begs the question”

      In any case, I was just talking about that very specific claim of yours.

      Notice I wasn’t challenging this:
      “ You must update your credences on the basis of P because of the Bayesian argument. Only then will you get the right answer from the ensemble argument”

      But rather your claim that
      a) RMT begs the question,
      and that
      b)it is legitimate to discard the analysis on the basis of what most physicists believe (which I still dispute).

      I think most physicists believe that the multiverse explains fine tuning very well, but RMT believe the same thing! That’s not mutually incompatible with his claim about fine tuning.

      As for this:
      “ Also Alex, note that as I’ve added a fuller Bayesian argument leading precisely to the conclusion I’m trying to prove, I don’t think you can say any longer that the Bayesian argument and the ensemble argument can both be correct but proving different things.”

      I’ve looked at your analysis (briefly) and I don’t grant that what you say follows. You’ve shown that on the basis of O, we should modify our fine tuning credences. Our ensemble analysis doesn’t take into account O; therefore your conclusion is not incompatible with our conclusion that we shouldn’t take fine tuning into account. And of course we don’t believe that you should take into account the fact that P modifies whether O is the case (which is true); as being somehow indicative of the likelihood regarding your potentially being born in M or S.

      Good day.

      • Alex Popescu says

        I wrote: “that P modifies whether O is the case”

        I meant: “That P modifies the odds ratio of M to S regarding whether O is the case for either.”

        Where O is: a single fine tuned universe exists.

      • Hi Alex,

        Just catching up on your points.

        I’m not sure that the burden of proof is entirely irrelevant, but I agree that it is largely irrelevant, so not worth debating further. But just to explain why I bring it up at all, and only because I don’t want you to think me unreasonable, I think it pertains to the circularity argument — I contend that each of us could perhaps be cast as rejecting some assumption in order to show that the assumption is false. The burden of proof point is to suggest that the more intuitive/default assumption is preferred in such circumstances.

        > it doesn’t follow from “I have an argument that defeats RMT’s points” that “RMT begs the question”

        Agreed in general, but my claim is that my argument defeats his because I think I show that RMT’s points implicitly assume that credence shouldn’t be updated because he doesn’t use the updated credence in his model, which is begging the question because whether credence should be updated is the question he is trying to answer.

        > So whether we should take your Bayesian analysis into account has no bearing on whether the ensemble is invalid as you claim. At best, if you are correct, then the assumptions of the analysis are incorrect (it is unsound).

        I see. What I was getting at is that it is an invalid model of the question we are trying to ask. I’m not sure if invalid is the correct word, due to confusion between valid/sound. Inapplicable might be better. It answers the question “if M is a country and S is a country, and the population of S is x and the population of M is 1000000x, then what effect does x have on our credence that we will be born in M or S?”, and it correctly and soundly finds that the answer is “no effect at all”. But this has nothing to do with the point he is trying to prove, because unlike the above case M and S are not places we know to exist, and M and S are mutually exclusive, such that either it is possible for anyone to be born in S and nobody in M, or it is possible for anyone to be born in M and nobody in S, and x is related to the credence of each case.

        > I’ve looked at your analysis (briefly) and I don’t grant that what you say follows

        Great. That’s what I was hoping for, that by laying it all out you would be able to show my mistake.

        > You’ve shown that on the basis of O, we should modify our fine tuning credences.

        I don’t think that’s right. Depends what you mean by “fine tuning credences”. You mean our credences as to what the value of p is? But I’m taking the value of p as evidence informed by cosmologists. My intention is to show that on the basis of O and p, we should modify our credence in M. I’m not sure what to make of the rest of this paragraph. It’s hardly a strength of the ensemble argument that it doesn’t take O into account. Perhaps you could instead point out which step or inference or assumption or definition in my detailed argument is faulty?

  3. Hi Alex and Dmitriy,

    I’ve had what I think is a very important insight.

    The best critique of my argument from you is that I have ignored evidence.

    But the ensemble argument ignores much more. If you think about the ensemble argument carefully, you’ll see that at no point does it make use of the fact that we know that any fine-tuned world exists. This completely invalidates it.

    To make use of this knowledge, you would need to do the Bayesian analysis and then update the weights as I have suggested.

    • Alex Popescu says

      In other word, your Bayesian analysis, if it’s really the most relevant application to answer the question of whether fine tuning should modify our credence in M (the ultimate question), as opposed to our ensemble about the likelihood of being born in either M or S; then that doesn’t lead to the conclusion that we should update our credences on the basis of fine tuning in the ensemble.

      It would still be illegitimate to update the credences for the ensemble, because the ensemble analysis does not take O into account.

      Rather, you are just showing that the assumptions of the analysis, namely that it’s the ratio of observers that really matters in answering the ultimate question, are bunk. Showing, in other words, that we should adopt your Bayesian analysis as the most relevant translation of the ultimate question, and leave it at that.

      Of course I don’t think your Bayesian analysis is the correct translation; it seems to me that answering the question of where we are more likely to be born has more bearing on the ultimate question, than just asking what is the probability that a single fine tuned universe would exist.

      Best,

      Alex

      • Alex Popescu says

        Of course one can still maintain that if your Bayes’ is the correct translation, then we really need to take O into account. But this just means discarding the assumptions of the ensemble about the ratio of observers, and installing some new row in the table of calculations that represents the likelihood that a single fine tuned universe exists. Then we would reach your same conclusion that P modifies the odds ratio.

        But notice that by doing so we have completely changed the ensemble analysis from being about a ratio of observers. Hence, it wouldn’t make sense to say that we should keep the ensemble in its original form (where it doesn’t take into account O), but still modify our credences/odds ratio because of the analysis you did which took into account O.

        I hope you can see that. What that means is that ultimately your analysis can never be about the ratio of observers in M or S. And therefore it can never ask or answer the question of whether we are more likely to be born in M or S. It should be somewhat obvious (if you are granting the selection effect); that the latter question is more relevant to the ultimate question than your Bayes’ analysis.

        So you can go back to attacking the assumptions of the analysis itself (i.e. we have to invoke actuality), but that’s different from saying that it wouldn’t answer the ultimate question if sound.

      • Hi Alex,

        > where we are more likely to be born has more bearing on the ultimate question, than just asking what is the probability that a single fine tuned universe would exist.

        I think these are the same question, although I understand this is not obvious. To explain why would be a thread 2 matter though, because I would need to explain what is wrong with how the ensemble argument models “where we are more likely to be born”. But you can make your point on thread 1 by showing where the Bayesian argument fails.

  4. Alex Popescu says

    I should clarify that when I say this:
    “ What that means is that ultimately your analysis can never be about the ratio of observers in M or S.”

    That I have in mind “normal observers”. For example, people who could have born in any universe (the selection effect). So you can definitely still ask the question about O, and maintain that the ensemble is about the ratio of observers being born in either M or S, as long as you stipulate that your observers are special. That for example they couldn’t have been born in other fine tuned universes; or that the conditions of M are rigged in such a way that it can only spit out (for instance) one fine tuned universe, no matter its size.

  5. Hi Alex,

    I’m going to sleep (hopefully) shortly, so I’ll get back to most of your comments, but there’s one thing that’s glaring.

    > What that means is that ultimately your analysis can never be about the ratio of observers in M or S. And therefore it can never ask or answer the question of whether we are more likely to be born in M or S.

    I’ve hinted at this before, but I think I need to remind you that this is not China vs Chile, which we know both exist and are not mutually exclusive (in the sense that while one person can’t be born in both, it is possible for different people to be born in both). M and S are not like this, but you’re treating them as if they are.

    Whether we are born in M or S depends on whether it is actually possible to be born in M or S respectively, and if it is actually possible to be born in M then it is not actually possible to be born in S and vice versa. Since we don’t know whether it is actually possible to be born in M or S we fall back on epistemic possbility, and for that we need to first consider credences, which are influenced by the Bayesian argument.

    Now, you can perhaps roll credences into your model by adjusting the ratios accordingly (I’m not sure it’s all that straightforward, as I illustrated in my analysis of Narnia vs Lichtenstein), but you need to put them in there somwhere. The brute numbers of observers in M vs S is actually less significant.

    The ratio of observers is not the only thing to consider to answer if we are more likely to be born in M or S, and in fact is perhaps irrelevant, unless I’m missing something. What matters instead is whether M is true or S is true, and this has nothing to do with the ratio. The ensemble proposed by Dmitriy is simply the wrong model for this question.

    • Alex Popescu says

      All of your points have been addressed; regarding whether we took credences into account by assigning a coefficient (we do). Whether your Narnia and Lichtenstein example (regarding the problem of infinities) should mean that we should abandon reasoning based on N, and what the consequences of doing so are. I.e. if we abandon reasoning based on N, should we reject the ensemble and adopt your Bayesian analysis? The answer is no, since your Bayes’ too relies on N (I explained this in more detail a few posts ago).

      And this point: “and for that we need to first consider credences, which are influenced by the Bayesian argument”

      I of course addressed in my very last few posts.

      I also addressed the following quote in the very beginning, and it is unfortunate that you are still repeating this claim: “ Whether we are born in M or S depends on whether it is actually possible to be born in M or S respectively, and if it is actually possible to be born in M then it is not actually possible to be born in S and vice versa”

      Finally, you argue that the China and Chile example are not analogous, because in that case it is possible for some observers to be born in both China and Chile (but not in both S and M). But I think this is irrelevant. Why? Because the ensemble only relies on it being possible for a single observer to have been born in either S or M. Meaning that all observers in S could have possibly been born in M, and vice versa. So long as those conditions are met; it follows that we can reason about the ratio of observers.

      And it is certainly true that a person born in China could instead have been born in Chile (i.e. we can do a counterfactual analysis, involving them being born in Chile, to ascertain the odds of where they were more likely to be born).

      Similarly, even if we stipulate that M and S observers are from the same population (they don’t have to be); we are just doing a counterfactual analysis of observers in S (asking, what if they were born in M instead?).

      I am too tired and too weary to continue reiterating the same points; because they were addressed in extensive detail in my other posts. No offense, but I get the sense that I am playing whack-a-mole here. This conversation has taken many turns, from arguing that we need to invoke actuality; to stipulating that we need to put M and S in a single population, to arguing that doing counterfactual analysis on a single population is incoherent, to the tangents about higher order logics and modal realism, and now to your Bayesian analysis, and of course much more.

      What is worse is that it appeared to me that you were conceding many of these points, or perhaps at least brushing them off as irrelevant to your actual argument at the time, but now you are going back to reiterating some of them again (i.e. about it being incoherent to do such analysis on a single population). The feeling that we have made no progress has permeated me throughout much of this conversation; which was why I earlier made the plea that you should think on the matter and try to stick with your best possible argument.

      I hope you do at least read the posts regarding your latest claim that we should update our credences on the basis of your Bayes’ reasoning. I urge you to do that and also think about how exactly you envision such ‘updating’ to work (i.e. would we have to change the ensemble too much to retain the belief that P modifies our likelihood of being born in either M or S?), and maybe reflect on my posts (when you are well rested) regarding why I think the two analyses are compatible. And why I believe that RMT’s and mine translate the ultimate question better.

      • Hi Alex,

        I have the same whack-a-mole feeling, believe me. But I think that’s just a feature of conversations like this. Interlocutor A makes a point, interlocutor B makes a counterpoint, and then A and B disagree about whether the counterpoint addresses the original point. It’s possible that A has misinterpreted B and it’s possible that B has misinterpreted A. These things are almost never satisfactorily resolved, unfortunately. So I completely understand your weariness. I think it helps to focus on specific questions each person doesn’t feel have been answered.

        > Whether your Narnia and Lichtenstein example (regarding the problem of infinities)

        It’s not really about infinity. It’s about how and whether population size should be factored in when the soundness of the assumption that such a population may exist is in question.

        > should mean that we should abandon reasoning based on N

        We should abandon reasoning based on N iff the two populations are mutually exclusive. If there is a possibility that both populations can coexist, then my Narnia/Lichtenstein example shows how to combine N and probabilities. If the two populations are both known to exist, then N is the only factor.

        I have to go now, so more later. In general, there’s a number of points you say you’ve already addressed, but I’m interlocutor A in this case. I don’t think you have. I will say that I have a better handle now on how mutual exclusiveness works, and how to contrast it with for example Dmitriy’s case of different possible configurations of particles in a room.

  6. So to sum up:

    The specific problems with the ensemble argument include:

    1. It ignores the evidence that we have observed that any fine-tuned world exists
    2. If the fact that this particular world is fine tuned as opposed to some other is important (I say it isn’t, Dmitriy says it is), then it ignores that too
    3. It treats the problem like China vs Chile, ignoring the fact that M and S are mutually exclusive (if M is just that more than one universe exists anywhere and S is just that only one universe exists anywhere — I hope we can agree to avoid complicating things by thinking about multi-level tiers of multiverses)

    These problems are there even if my Bayesian argument is also guilty of ignoring the evidence that this particular world is fine tuned.

    • Alex Popescu says

      Hey DM,

      Regarding your last; the part about mutually exclusivity I addressed in my latest post (along with the other claims in more detail). My latest post on the bottom summarizes everything in more detail; so please read that and see if you disagree with things and let me know.

      I will quickly discuss this however:
      “ It’s not really about infinity. It’s about how and whether population size should be factored in when the soundness of the assumption that such a population may exist is in question.”

      Okay, but this is just going back to your previous claims that we either need to invoke actuality, or that doing counterfactual analysis on a single population is incoherent. You yourself admitted that you couldn’t convey a clear reason to believe the former.

      I talk about this too in my latest post, as well as the premise that we should discard reasoning based on N because of the “mutual exclusivity” problem. I call your claim about mutual exclusivity “condition K”; so look for that. As for the actuality claim, if you still disagree (after reading my latest post) about our needing to invoke actuality; I would really appreciate it if this time you did in fact bring forth that argument you were talking about which we never addressed. Where basically you said that you just wanted to put forward your claim about actuality to see if it was contested, but didn’t give the actual argument.

      Well, if you continue to maintain this claim; now is the time for bringing forth the best argument you can think of for doing so. If on the other hand you’re just repeating your belief that quantifying over a single population is incoherent; then note that (to spare both of us from getting into that again) I showed that you don’t actually need to draw the observers of M and S from the same population (also in my latest post). So I’d appreciate it if, when you had the time, you addressed those things.

      Best,

      Alex

  7. Hey DM,
    “The best critique of my argument from you is that I have ignored evidence.

    But the ensemble argument ignores much more. If you think about the ensemble argument carefully, you’ll see that at no point does it make use of the fact that we know that any fine-tuned world exists. This completely invalidates it.”
    Let’s tackle this with a super simple example from Steven’s forum, where I am trying to walk someone through some increasingly complex scenarios to jog their intuition about anthropic reasoning (http://disq.us/p/2fk5soj if you want to check it out):

    Imagine you are sleeping in a hospital overseen by Dr. X. Suppose the doctor flips a coin, and if it lands heads he lets you live and you eventually wake up, and if tails he only lets you live with a small probability q, otherwise he annihilates you. You agree that if you wake up you should conclude it probably fell heads right? (assume you know the setup of course).

    What odds should you assign to heads vs tails if you wake up and realize you have not been erased from existence? I hope you would agree they should be 1:q for heads:tails, right?

    How can you establish that? One way would be a Bayesian argument, with the evidence being E = I am still around. An alternative way would be with an ensemble. How would that work, and how do I use evidence E here?

    Remember EP = answer is unaffected by whether similar experiments are performed on other versions of Earth somewhere in galaxies far far away.

    So let’s then assume, like we did with room X, that there are G copies of Earth with their own DM’s undergoing similar experiments, 0.5G where the coin fell heads and 0.5G with tails.Some DM’s survive and have therefore property E. You know you are one of them, **because you know you have property E**, but you have self-locating uncertainty as to whether you are on an Earth with the coin being heads or tails (property H or T).

    What odds should you assign to having property H vs T. Since you are equally likely to be any DM with property E, they should be the ratio:

    H:S = [num. DMs with E&H] : [num. DMs with E&T] = 0.5G:0.5Gq = 1:q.
    I hope this makes it clear how evidence (E in this case) enters into the ensemble analysis.

    • Hi RMT. Very briefly, because this seems to be on thread 2 (ensemble) and I’m hoping we can focus on thread 1 (what’s wrong with the Bayesian argument).

      > I hope you would agree they should be 1:q for heads:tails, right?
      Right.

      > An alternative way would be with an ensemble.

      You can, but this is simpler than S vs M. In S vs M we have two variables attracting our attention, both p and N. I think the relevant one is p, you think it is N. For this simpler thought experiment, there is only q. Though q is a probability, you can translate it into a ratio between two populations of different sizes and pretend that both populations exist, like China vs Chile. This works because it is a simple case with no confounding factors — there is some complex formula I haven’t derived yet (but could, I feel) where some subformula we must multiply by evaluates to 1 and the whole thing becomes a simplified special case. I don’t think it works in the case of S vs M because now you have two populations of different sizes each of which may or may not exist with different probabilities and the simplification doesn’t happen.

      I also don’t agree that your account shows you’re taking O into account, but I feel that’s a thread 2 digression so I won’t get into it if you don’t mind.

      • Alex Popescu says

        Hey DM,

        “ I also don’t agree that your account shows you’re taking O into account”

        You’re going to have to address this, because RMT’s point about your analysis not being applicable rests on the fact that the ensemble/Bayes analysis involving E (as opposed to just O) is the most applicable setup.

        RMT is trying to demonstrate that,
        1) if condition EP holds, and
        2) if the ensemble takes into account all relevant evidence, it follows that
        C) we can’t use your Bayesian analysis to argue that we need to modify our credences for the total evidence case.

        Assuming that you agree that we need to take all the relevant evidence into account; you must tackle RMT’s assertion that O is entailed by E, and is taken into account by the ensemble and also the Bayes reasoning that he gave in his last posts. So you’re challenging step 2 in his argument. We can’t separate thread 1 and 2 so neatly as you think for that reason.

  8. Alex Popescu says

    Hey Dmitriy and DM,

    I think that DM was saying that the ensemble does take into account some E, but that this E is not the evidence that a single fine tuned universe exists. But we do in fact take into account fine tuning before and after in the ensemble, and that is motivated by the evidence that we are born in such a universe (the degree of P can be set by our observations in our universe).

    Also, to add onto to RMT’s point, where he shows that if you have self-locating uncertainty then the odds of being born in one place are influenced by the size of the potential observers (so N matters), we now have to tackle whether it is legitimate to engage in reasoning regarding whether we could have been born in either M or S.

    Firstly, I don’t think it follows that we can’t be speaking of physical possibility on the grounds that M and S are ‘mutually exclusive’ in the sense DM mentioned (of course it might make sense to deny physical possibility if we don’t have any evidence for M). Because as mentioned, if modal realism is true as DM claims, then you definitely can have two different classes of population in M and S, such that it is true that K:“different observers are living in both M and S at the same time” is met.

    Let us call the lack of condition K your main stipulation against why we can’t ask whether we are born in M or S. In my above posts, I showed why this stipulation is false (because we can engage in counterfactual analysis using one single population), but it is also irrelevant because we can draw on two different populations for our analysis.

    And this holds true if we are just arguing about epistemic possibility; in that case we don’t need to take on modal realism to argue that condition K is satisfied. I already earlier showed that we can use two different possible (not actual) populations to represent observers in M and S.
    As long we believe: ◇Ex(Mx) & ◇Ex(Sx)

    Which just reads; possibly some observers are born in M and possibly some are born in S. This takes into account epistemic possibility, and it meets condition K since some observers being born in both does not entail that they must come from the same population.

    So it is just like China and Chile; the only difference is that China and Chile are actual whereas we presuppose that M and S are not actual entities in our analysis (but as you see; that does not stop K from being fulfilled). Hence, K is both not necessary but also simultaneously can be fulfilled anyway.

    Naturally, you can go back to claiming that we really are taking on the burden of invoking actual entities, but I think that would be seriously unhelpful because we have been extensively over that matter and you could not (you admitted) invoke a clear reason to do so.

    All that being said, I suggest we stick with the Bayesian ‘updating’. In my previous posts I suggested that we can’t update our ensemble analysis with the results of your Bayes’, because they take into account different things. One asks whether P modifies the odds ratio between the ratio of observers being born, and the other whether P modifies the odds ratio regarding the question of O (single fine tuned universe existing). They are answering different questions that are fully compatible, and you have failed to prove that they are not (a necessary prerequisite for any updating).

    Therefore, this really does boil down to whether it is more appropriate to ask “are we more likely to be born in M or S”, or whether it is more appropriate to ask about single fine tuned universes.

    So let’s separate this into various portions:

    1)Whether it makes sense to ask if we could have been born in M or S (is condition K satisfied; is it even necessary?)

    2)Whether your Bayes’ is incompatible with our ensemble analysis (which is a necessary prerequisite to saying that we should change the ensemble conclusions on the basis of your analysis).

    3) Whether your point about us not taking into account that a single fine tuned exists has merit. We do take that into account, in our analysis P is the degree of fine tuning, which is given by the observations of the fine tuning in our universe.

    4) Whether the question of being born in M or S better answers the ultimate question, relative to your Bayes. This is fundamentally the key one, because eliminating perceived problems with the ensemble doesn’t matter if you don’t think it accurately translates the real question. Again, I’ve assumed it somewhat obvious that whether we are more likely to be born in M or S (assuming the question has validity) is most relevant to answering the question at hand.

    That’s because if we find out at the end of the day that P makes us no more likely to be born in M; then by definition that is the same as saying that our credences in M were not changed. The whole point is that we have self-locating uncertainty as RMT said, and so the question of where we are likely to be born has direct bearing on the likelihood of that location to exist.

    If after you have read this it still happens that you have objections to one of these statements (or something else), please let us know by referencing which part did not convince you.

  9. Hey Alex andDM,
    I think I understood most of the above. I am trying to simplify things as much as possible without sacrificing rigor, so I am curious if you agree that it is deductively provable that:

    Theorem 1. If EP is true for any given problem, then the ensemble analysis gives correct credences, i.e. credences after accounting for all of the agent’s available data/evidence E.

    Here EP is defined as: correct credences for the given problem are unaffected by whether or how many similar completely independent experiments are performed in different places, and it’s assumed by that that:
    – in some possible world they are performed many times (call this condition K2, stronger than K)
    – credences for an agent having total evidence E in a world where they have self-locating uncertainty are determined under the assumption that the agent is equally likely to be any agent in that world that satisfies condition E

    My example above was supposed to illustrate exactly how the analysis works by simply counting observers in the ensemble that have the same evidence we have. I have other points I wanted to make about K etc. but wanted to first double check that you agree that theorem 1 is deductively provable, and that for any problem **in which its precondition holds** the ensemble analysis would therefore be immune to objections like:
    “The specific problems with the ensemble argument include:

    1. It ignores the evidence that we have observed that any fine-tuned world exists
    2. If the fact that this particular world is fine tuned as opposed to some other is important (I say it isn’t, Dmitriy says it is), then it ignores that too
    3. [essentially asserting K2 is false for the multiverse question]”

    Of course we can and must say more about whether the precondition holds but just wanted to first make sure everybody can agree to the above.

    • Alex Popescu says

      Hey Dmitriy,

      Oh I completely missed the EP part in your last; my apologies. Yes we agree then that the Bayes’ analysis shouldn’t update our credences for the ensemble. Your EP claim is much stronger, staying that no Bayes analysis using just evidence collected on earth can refute it. But notice it does entail certain things like the fact that we could have possibly been born in M etc…

      So if DM disputes this, which I think he does, we perhaps can’t reason to the above. Nevertheless, it’s at least informative to show that the burden of proof is on DM to demonstrate that the Bayes’ analysis showing (P modifies) is incompatible with the ensemble analysis showing (P doesn’t modify). Because such incompatibility is necessary to reach the conclusion that we should update our credences (i.e. reject [p doesn’t modify]).

      I’ve laid out all the other possible steps in my latest post above; so that we don’t lose track of things. Unfortunately, this does excessively complicated the picture.

  10. Alex Popescu says

    Hey DM,

    I don’t want to distract you from my latest post; it’s best if you just concentrate on that since it summarizes everything. I quickly wanted to clarify this:
    “ It’s hardly a strength of the ensemble argument that it doesn’t take O into account”

    Note there’s a difference between evidence and hypothesis. Our ensemble isn’t trying to prove the hypothesis of O; in other words it’s not trying to show how likely it will be for a single universe to exist. But it does take into account evidence that a fine tuned universe exists (see my point 3). So it’s not true that the ensemble analysis is “weaker” on these grounds; I think you confused what you are trying to show with what counts as evidence.

    The point about it not relying on O was just that it’s answering a different question/searching for another hypothesis.

    • Alex, actually I believe O is not that, it’s defined as the evidence that at least one life-permitting universe exists. But of course the ensemble analysis does take O into account, because the total evidence E that each member of the ensemble satisfies (assuming the ensemble is possible, but that’s a separate objection) entails O for that member.

      To put it simply, property E implies property O.

  11. Hey Alex,
    I either misunderstood or disagree with
    —–
    Your EP claim is much stronger, staying that no Bayes analysis using just evidence collected on earth can refute it. But notice it does entail certain things like the fact that we could have possibly been born in M etc…

    So if DM disputes this, which I think he does, we perhaps can’t reason to the above.
    —–
    1. Thm1 says even more, that if EP, then the ensemble analysis that uses ALL evidence the agent has (though it’s fine if it ignores evidence that is stipulated or proved irrelevant) gives the correct credences. Do you agree that it says that and that it’s provable (since it’s almost tautological)?

    2. That of course entails that if EP then “no Bayes analysis using just evidence collected on earth can refute it” Unless you mean future evidence.

    3. Do you agree that so far, in the above post, EP is just a definition, no claim is made yet for which problems it is true?

    4. EP, **applied specifically to the multiverse question, if true ** would mean that “we could have possibly been born in M etc…” But again so far the above post is not asserting EP’s truth for any problem.

    5. “So if DM disputes this, which I think he does, we perhaps can’t reason to the above.” He doesn’t dispute that, he disputes that in some possible world there are people living in M as well as people living in S. In other words he denies K2 for the multiverse question.

    6. Crucially though he doesn’t deny K2 for other analogies used by Steven and Philip. He accepts that we can use ensemble analysis in thermodynamics, and I think agrees that you can have an ensemble of Dr.Xs just as easily as a thermodynamic ensemble of room Xs. He only insists that K2 is false for the multiverse **in light of his definition of the word “multiverse”, so that wouldn’t apply to the IVF analogy.

    DM, of course please correct me if I didn’t represent fairly what we came to in our discussions of ensembles in physics and the crucial role of your specific definition of the word ” multiverse” in your denial of K2 for it.

    • Alex Popescu says

      Hey RMT thanks for that; I didn’t know that O was specifically construed as evidence. I thought that it was just the statement (there is a single fine tuned universe). Which of course can be construed to be evidence, but it can also be the thing we are trying to prove for either M or S. In which case, P does modify the odds ratio regarding the likelihood of the statement being true in either M or S. So my apologies DM, if you are reading this; then substitute the above statement for any time I said O.

      Regarding EP being a definition; yes I meant that in order for the assumptions based on EP to be sound (i.e. we shouldn’t modify our credences if we take all the evidence into account) we need to assume that it is possible for an observer born here to have been born in M. Is this not so?

      As for whether DM assumes that; well DM if you can clarify this point that would be really helpful. I thought his argument about the incoherence of the analysis involving a single population was meant to show that a real observer in S can’t have possibly been born in M. Unless I’m mistaken of course.

    • Alex Popescu says

      Naturally I do agree with your conclusions Dmitriy; I’m just not sure if DM accepts that it is possible for an observer in S to be born in M. And I agree with your take on what the EP claim is really about (and yes I meant my interpretation of the claim to be about any possible evidence on Earth). Hopefully DM will clarify his position, and my apologies if I have misconstrued his stance on that point.

      I’m any case, regarding DM’s latest post, would you agree with my analysis that DM’s argument is both valid and sound (i.e. p does modify the odds ratio for M and S regarding the likelihood of the statement O, as I defined it, to be true)? Which is the same as saying that we should update our fine tuning credences in his Bayes’ analysis, on the basis of O alone. Of course, that doesn’t show that we should always update our credences, and I think you’ve proved that we can’t do so once we take all the evidence into account.

      So I see this as just a problem of DM’s analysis not being applicable to the final question. You showed that it’s not applicable to the ensemble, and we shouldn’t use the conclusion of DM’s Bayes analysis to update our credences in that case; which of course I agree with.

      But we have a further task in light of DM’s statement, which is to show that our ensemble more appropriately captures/represents the ultimate question which is “should fine tuning modify our credence in M?”, and to show that his analysis does not. I of course think that we did so. But would you agree that’s the general order of things as I laid them out?

      P.S. did you get that email I sent you today?

      • Alex Popescu says

        So basically to sum up; all we need to do is see if DM believes that it is possible for an observer born in S to be born in M. If not, then your analysis is sound. Once he sees that, it obviously follows that the ultimate question, “should fine tuning update our credence in M” is resolved (thanks for proving that).

        If the answer is no, then we have to explore those issues.

      • Alex Popescu says

        I meant “if yes, then your analysis is sound” of course.

  12. I may not have time to respond in detail for a while.

    I just wanted to give a quick note to describe where I’m at and lay out how I see the structure of the argument.

    There are two threads here (1) whether the Bayesian argument is valid/sound/applicable and if not what’s wrong with it and (2) the same for the ensemble argument. I feel my strongest argument is (1), to defend the Bayesian argument and invite criticism. But it’s also interesting to explore (2) what may be wrong with the ensemble argument. But from my point of view that’s a side issue. I’m happy to set that aside if you are. As far as I’m concerned we should be able to answer the question from the Bayesian argument alone — either it shows what I want it to show or it doesn’t. If we ever do reach agreement on that (and I realise this is vanishingly unlikely), then we could explore whether the ensemble argument makes sense.

    I completely understand how Alex is vexed that I’ve apparently admitted my arguments are incoherent and now I’m bringing up the same arguments again. From my perspective, I’ve admitted that I haven’t expressed my position very coherently, and I’ve allowed that my ideas may not work. But now I’ve had some new insights and I’m better prepared to explain what I’m talking about with regard to mutual exclusivity etc. But these issues pertain to thread (2) rather than thread (1), so perhaps they’re better dropped for now.

    • Alex Popescu says

      No worries DM; when you have time please read over RMT’s and my posts carefully. Because we do address your stuff (for instance I write about your mutual exclusivity claim), and you might miss that. Just to make sure we aren’t talking past each other

      • I certainly would like to. However, in the interests of getting this conversation under control, and if it’s OK with you, I’m now thinking of dropping thread 2 for now, which would include your points on the exclusivity claim, Which means I may be answering RMT more than you as you’re mostly responding to points on thread 2.

        If you do particularly want me to address your points on thread 2 let me know and I will.

    • Alex Popescu says

      Yes, it seems that RMT has shown quite nicely that your Bayes’ analysis is inapplicable (we think so). I would stick to that for now. Of course in the end if you agree with the conclusions; then we would need to show that the ensemble analysis is the appropriate one for taking all relevant evidence into account.

      But I think that is easily demonstrable, because it takes everything that your Bayes’ takes into account as evidence and more. And further, the claim that taking all evidence into account is best for resolving the ultimate question, is, I suppose, obvious.

      If after all that you still wish to dispute the ensemble on the grounds that it’s not really the analysis that takes all relevant evidence into account (i.e. your mutual exclusivity claims) then read my posts and then just let me know.

      Best,

      Alex

  13. I can say more later but here’s perhaps a crucial point DM is not yet seeing:

    Given a choice of evidence (E vs O vs some E9) V, **the ensemble analysis and the Bayesian analysis give the same result!**

    They are basically different forms of the exact same calculation. Think about how you would prove Bayes theorem, think about the underlying fundamental assumptions required.

    The difference between the two results we are getting have nothing ultimately to do with the fact that (1) uses Bayes and (2) uses an ensemble. The difference in the answers is because you are updating on V = O and we are updating on V = E (minus perhaps evidence that is stipulated to be irrelevant, like my height)

    • Alex Popescu says

      Yes, I think in addition to that; DM might have confused our not asking about whether “a single fine tuned universe exists”, as itself being indicative that we are not taking such a thing into account as evidence. I’m not sure how else he arrived to the latter conclusion. Also, about the email; I wrote a comment on your site about that. Thanks.

  14. Hi guys,

    I had wanted to focus on thread 1 (whether the Bayesian argument works), which I feel is my best argument, less explored, and the more tractable of the two. However all the points you’re making seem to be on thread 2 (whether the ensemble argument works). I’m not really seeing any significant points agains the Bayesian argument since Dmitriy suggested I wasn’t using all the evidence. I responded to that but haven’t seen much of a response to my response.

    So, as far as I’m aware, the only point you have against the Bayesian analysis is that I’m not taking all the evidence in, and specifically I’m ignoring the fact that our particular world and not just any world is fine tuned? Am I understanding you correctly?

    To be specific, the bit I don’t think you’ve responded to is from the top comment on this page, starting “Point B is more interesting” and continuing until “the issue is entirely decided by how we ought to think of personal identity”.

    Perhaps you think this stuff has been addressed but it’s not clear to me that it has.

    BTW, I don’t want to imply that I think the Bayesian argument gives the right response just because it is a Bayesian analysis and the ensemble result gives the wrong result just because it is an ensemble analysis. My position is just that this particular Bayesian analysis is perfectly cromulent and gives the result I want (while on thread 2 arguing that there are problems with how this particular ensemble analysis is conducted).

    If you’re more interested in thread 2 then I guess it would help to pick a particular topic to focus on. I think I’d like to talk more about what I mean about mutual exclusiveness and whether China vs Chile is a good analogy if so. You’ve made points on this topic I should address. But again I think thread 1 may be more tractable as everyone seems to acknowledge that Bayesian analysis is applicable if conducted correctly, whereas I’m not as convinced that ensemble analysis makes sense in this case (though I’m not asserting that it wouldn’t if conducted correctly).

    I feel you may want me to deal with the EP stuff and “it is possible for an observer born in S to be born in M.” , but I sense that becoming a morass because it looks to me like these questions are bound to get tangled up in confusion over what we mean by “possible” and different levels of possibility, e.g. whether it is possible that something is possible etc. I don’t have ready answers for many of these questions because I’m not clear on what you’re asking. The Bayesian argument seems much more clear cut to me.

    • Alex Popescu says

      Your artificial attempt to separate thread 1 and 2 complicates rather than simplifies I believe. That doesn’t mean that we have to get into all of your proposed problems regarding our ensemble. Because as RMT mentioned, we can just do a Bayes analysis which relies on E that yields the same conclusion (fine tuning doesn’t modify the credence in M). The bottom line is that there are two ways to answer this question.

      Either we can approach the matter more formally, as RMT did; wherein we realize that we can construct an ensemble/Bayesian analysis that would show that fine tuning does not modify the credence for M, so long as we take evidence E (we exist) into account. Where our ensemble specifically asks, given that we exist, where were we more likely to be born?

      We can also construct an ensemble/Bayes analysis that shows that fine tuning does modify the credence for M, so long as we take O (instead of E) into account. Where O is the evidence that there is a single fine tuned universe. But notice that E entails O, and by the total evidence requirement that Goff and White themselves invoke, it follows that our analysis is more preferable.

      The second method, which is simpler, is the one I’ve been saying all along. It only makes sense to update our credences on the basis of fine tuning in our ensemble case, if you can demonstrate that your Bayes analysis is contradictory to it. The burden of proof is on you to do so.

      I think this latter method is easier and more simple to understand; let’s not get into the total evidence stuff if you don’t want to. But the key is that no one is saying that your Bayes’ is wrong/invalid, so you’re asking the incorrect question here; we’re just disagreeing with you concerning it’s applicability.

      Notice that I think that both statements
      “fine tuning modifies the odds ratio between M and S regarding the likelihood of a single fine tuned universe existing”

      And
      “Fine tuning doesn’t modify the odds ratio between M and S concerning the likelihood of our being born in either”.

      Are fully compatible. It’s up to you to demonstrate that they are not. And if you go over our posts again, you’ll see that we (I) made many points regarding both why they are not contradictory, and also why the latter question is the better translation.

      • Alex Popescu says

        I want to elaborate more on the non-contradictory aspect. Perhaps you did not get a good sense of what I meant when I said that we can update our credences for M in one case but not the other. That’s because both cases are demonstrating different things. Your case demonstrates that fine tuning makes the odds ratios more favorable for M; regarding the likelihood that a single fine tuned universe exists (call this L).

        But should this really raise our credence for M? Only if you believe that the fact that p demonstrates that M becomes more relatively likely to instantiate L; is itself evidence that M is more likely. But why should we believe this? That is the key, you need to demonstrate applicability.

        In other words, I’ve been granting the jump from your demonstration concerning the impact of p on the odds ratio, to the credences about M. In part because I’ve been implicitly assuming that we can construct a new ensemble showing that the ratio of relative observers increases for M in proportion to P. And this is true, but only if we believe that that the ratio of observers is somehow tied to the likelihood of a single fine tuned universe being instantiated.

        As China and Chile show; this isn’t the case (yes I know this is a thread 2 issue). You don’t have to address that last, but note that there is a real issue here of applicability that you need to address.

      • Alex Popescu says

        One final clarification, because it might appear I’ve said different contradictory things at times.

        I believe your Bayesian analysis (based on O) with respect to the odds ratio for M:S changing in proportion to P, is both valid and sound, but not applicable.

        I also believe that your Bayes analysis conclusion regarding our needing to modify the credences for M (more favorably) on the basis of P, which goes one step further, is valid but both unsound and inapplicable.

        That’s because the jump from (odds ratio is modified by p) to (p modifies credences for M) relies on the fact that O is somehow linked to the likelihood of M or S existing.

        You need to demonstrate this link in order for us to accept your final conclusion (that we need to update our credences for M because of P). You did not adequately do so in your original Bayes’ analysis, because you simply assumed the step was intuitive (but of course it’s not).

        It is not enough to stand back and say that we are obligated to pick holes in it.

  15. Hi Alex,

    Thanks for this.

    > Your artificial attempt to separate thread 1 and 2 complicates rather than simplifies I believe.

    Fair enough. I’m just trying to prioritise, and go with my strongest argument, as you suggest. I’m willing to discuss other points if you feel they’re crucial.

    > we can just do a Bayes analysis which relies on E that yields the same conclusion (fine tuning doesn’t modify the credence in M).

    Please do so then. You can take mine as a template, perhaps. So far, it seems you have just been asserting that such an analysis exists and would yield the conclusion you expect. I’d like to see it, because it isn’t obvious to me. It might make the differences in how we are thinking of the problem clearer.

    > The second method, which is simpler, is the one I’ve been saying all along.

    I don’t see how it’s simpler, if I understand correctly. The first method is to conduct a Bayesian analysis on E. The second is to conduct a Bayesian analysis on O, then realise that O implies E, and then to conduct a Bayesian analysis on E instead. I suggest that you just conduct a Bayesian analysis on E.

    > Only if you believe that the fact that p demonstrates that M becomes more relatively likely to instantiate L; is itself evidence that M is more likely. But why should we believe this?

    I don’t understand why you’re introducing the term L when what you’re describing seems to be covered by O. Or is L supposed to be P(O)? I don’t think P(O) without givens is sensible as O is just an observation. Perhaps I’m missing something. I’ll interpret this as if you mean O.

    I’m finding it hard to parse your language here. Here’s an attempt to formalise what I think you’re saying. I hope WordPress doesn’t eat it as it contains less thans and greater thans.

    “p demonstrates that M becomes more relatively likely to instantiate L;” : P(O|p=p1 & M) > P(O|p=p2 & M) where p1 > p2, e.g. the probability of a multiverse producing an observer-supporting world if p is 1 (no fine tuning) is greater than the probability a multiverse producing an observer-supporting world if p is 10^(-9) (fine tuned), all else being equal.

    This is a bit complicated to deal with. But I had a step asserting that P(O|S) is equal to p, which I think straightforwardly means P(O|p=p1&M) = 1 – p1, at least if P(M) = 1 – P(S) as I assume in the argument.

    “is itself evidence that M is more likely”

    That’s just using Bayes Theorem to turn our P(O|M) above into P(M|O), which is equivalent to P(M) since we know O is true. This is exactly what I did in the Bayesian argument, isn’t it?

    > And this is true, but only if we believe that that the ratio of observers is somehow tied to the likelihood of a single fine tuned universe being instantiated.

    I would say that whether it makes sense to think in terms of the ratio of observers at all is itself a thread 2 issue. It’s not directly related to the Bayesian argument. I feel you should be able to show a problem with the Bayesian argument without appealing to the fact that it doesn’t affect the ratio of observers, because the conclusion is just that a lower value of p should increase our credence in M, which seems to me to be what I need to show. Either it isn’t, or I’ve made a mistaken assumption, or I’ve left out some evidence, or some inference doesn’t follow, or the conclusion doesn’t mean what I think it does. The fact that it doesn’t meet some other constraint you want to impose doesn’t tell me what’s wrong with it, although it may suggest that it is wrong. If you don’t know what’s wrong with it that’s fine — that could be reason to focus more on thread 2.

    > You need to demonstrate [that the jump from (odds ratio is modified by p) to (p modifies credences for M) relies on the fact that O is somehow linked to the likelihood of M or S existing] in order for us to accept your final conclusion (that we need to update our credences for M because of P). You did not adequately do so in your original Bayes’ analysis, because you simply assumed the step was intuitive (but of course it’s not).

    Can you identify which specific step in the argument needs justification? I took you all the way from assumptions to final conclusion, so if I’m missing a step it must be somewhere in the formal argument.

    My best guess is it’s this step:

    6. P(O|S) = p (From (vi) and the definitions of p and O)

    Because this step gives the probability of observing O given that S exists, which is sort of a link between O and the likelihood of S, I guess, and perhaps it’s not immediately obvious how I got this result as it relies on combining three separate definitions and assumptions.

    Let me pull in all the relevant definitions and assumptions.

    p: (fine tuning parameter): the proportion p of possible universes that support observers
    O: The hypothesis that there exists a universe which supports observers (is fine tuned).
    (vi) is that on S, the single actual universe is randomly chosen (according to a uniform distribution) from our population of N possible universes.

    Perhaps I’m missing something, or this is not the step you take issue with, but it seems pretty obvious that if one universe is chosen according to a uniform distribution from a population of N universes of which p * N are observer-supporting, then the the probability that the chosen universe is observer-supporting is the number of observer-supporting universes divided by the number of universes, or p*N/N = p.

    Would it be helpful if I redid the argument to take Dmitriy’s criticism A into account (this was the one about how I should translate the notion of fine tuning increasing credence into formal notation)?

    > It is not enough to stand back and say that we are obligated to pick holes in it.

    The focus on thread 1 is just an attempt to follow your suggestion to focus on my strongest argument. If you don’t want to engage in that, then maybe we could discuss why I think the ensemble argument doesn’t work and Dmitriy could discuss why the Bayesian argument doesn’t work (for this particular problem).

    • I said:

      > I don’t think P(O) without givens is sensible as O is just an observation.

      I don’t think this is fair as I talk about P(O) myself too. I need to get my story straight. E1 is the observation. O is the hypothesis that some universe is fine-tuned. I’m still not sure what L means.

      • Alex Popescu says

        Hey DM,

        Very quickly since RMT seems to be on top of things. About the L; that’s just my fault. My apologies, I completely forgot about O already being defined; I have no excuse except for a mental slip-up. Even worse, I have previously used the variable K to mean something; only to realize that before me that you and RMT both had used the same variable to represent something else! So treat L as if it means O. Also this:

        “ The second is to conduct a Bayesian analysis on O, then realise that O implies E”

        Is the other way around. Not sure if that’s just an error of spelling on your part, but E implies O; not the other way around. Because of course if there were a fine tuned universe, that doesn’t guarantee that we would be alive. It’s precisely the fact that E implies O that is supposed to make it stronger.

        Finally your point here: “feel you should be able to show a problem with the Bayesian argument without appealing to the fact that it doesn’t affect the ratio of observers,”

        I addressed in my last post: “That’s because the jump from (odds ratio is modified by p) to (p modifies credences for M) relies on the fact that O is somehow linked to the likelihood of M or S existing.”

        So I completely agree with this point here:
        “ according to a uniform distribution from a population of N universes of which p * N are observer-supporting, then the the probability that the chosen universe is observer-supporting is the number of observer-supporting universes divided by the number of universes, or p*N/N = p.”

        But notice that doesn’t demonstrate that M is more likely to exist because of P! You’re assuming a leap from our credences about a fine tuned universe existing being partially based on p; to a conclusion regarding the credences of the multiverse existing being partially based on p. Should we really care about the probability of a randomly chosen universe being fine tuned; or should we care about our likelihood of being born in either?

        Again, I think it helpful to go back to the Narnia and Lichtenstein case; where your objections aside, you can perhaps get the notion why we feel that N is so important for M and S. Because realize that your argument also works for Narnia and Lichtenstein (i.e. substitute some value for p regarding the likelihood of being born), but doesn’t entail your conclusions regarding p affecting the likelihood of Narnia existing. My hope is that you can see from that case why we believe that N should matter, even if you think they are disanalogous.

        But I won’t say anymore for fear of derailing the promising discussion between you and RMT.

      • Good comments, Alex, thanks. In particular, you’re right that I got O and E backwards.

        To be honest, I’m a little sleep deprived at the moment as we’re planning an emigration from NZ to the UK, and it’s not a great time for that! Also it doesn’t help that I’m a little obsessed with this interesting discussion. But I’m making a lot of mistakes for which I apologise.

        > But notice that doesn’t demonstrate that M is more likely to exist because of P!

        No, this was just one step in an analysis, the conclusion of which was that M is more likely to exist because p is small. I’m not sure which specific inference I’m taking to be intuitive but you think is not. Or is it some general point that can’t be localised to a specific step?

  16. I don’t mind discussing just (1), and I think the one and only hole in it is that you are updating on O. Do you agree that E entails O? Do you agree that if updating on E gives a different result then that would invalidate updating on just O?

  17. Hi DM,
    I think you are right, the best way forward is I think to just show the Bayesian analysis using E. Before that though, there seem to be big problems with this part:

    This is a bit complicated to deal with. But I had a step asserting that P(O|S) is equal to p, which I think straightforwardly means P(O|p=p1&M) = 1 – p1, at least if P(M) = 1 – P(S) as I assume in the argument.
    [No, P(O|p=p1&M) = 1 – (1-p1)^N]

    “is itself evidence that M is more likely”

    That’s just using Bayes Theorem to turn our P(O|M) above into P(M|O), which is equivalent to P(M) since we know O is true.
    [O true doesn’t imply P(M) = P(M|O) at all]
    ******

    Just so we don’t talk past each other later, do you agree with the two corrections?

  18. Hi Dmitriy,

    > Do you agree that E entails O?

    I don’t see much difference between E and E1 in my analysis, and I said in my analysis that E1 implies O, so yes.

    > Do you agree that if updating on E gives a different result then that would invalidate updating on just O?

    That seems plausible in general. But with a caveat.

    Whatever it is that prevents you from being amazed that I just now generated (https://www.uuidgenerator.net/) the specific UUID 1fad1449-a315-45ca-a685-da0aea33794e against all odds may come into play. If you are not surprised that I generated some UUID (O) you should not be surprised that I generated a specific UUID (E), unless that UUID is very special for some reason. I expect you to agree with this, and perhaps you can explain why this is so more clearly than I (I’m sure there’s a name for this idea but it escapes me). Whether we ought to treat the observation as generic (O) or specific (E) then depends on whether the observation is special. If your argument explicitly or implicitly assumes that there is something very special about E which I don’t find special, I may reject it.

    > [No, P(O|p=p1&M) = 1 – (1-p1)^N]

    I have no idea now what I was thinking. My brain is fried. I think I got myself confused. Your correction looks right to me. I found it easier to work with S first and convert to M at the end.

    > [O true doesn’t imply P(M) = P(M|O) at all]

    Doesn’t it? If P(A|1=1) = 0.5, doesn’t that mean that we should have credence 0.5 in A? If not why not?

    • Alex Popescu says

      “Doesn’t it? If P(A|1=1) = 0.5, doesn’t that mean that we should have credence 0.5 in A? If not why not?“

      No, for instance P(O|1=1) is very low, but we shouldn’t conclude that P(O) is very low, if for example we knew M. That’s because P(O|M) is very high. Here O and M are the standard terms we’ve used. You shouldn’t assess P(A) until you’ve finished updating and taken all the relevant evidence into account (i.e. E).

      • Hi,

        I was just logging to say I think I realised (while washing the dishes) what’s wrong with P(M) = P(M|O) and I think it’s the same point Alex is making.

        If P(M) is the prior probability of M, before we start our analysis, then P(M|O) can be very different. But if O is true, then the posterior probability of M is just P(M|O). So I think the problem here is that we need notation for credence before and after an argument or evidence, which is why I was using C_prior(M) and C_posterior(M) in my argument. Is there a more standard way of denoting the distinction?

    • Alex Popescu says

      Also another point (sorry; I really should leave room for RMT to do his analysis), about this objection of yours:

      “ Whether we ought to treat the observation as generic (O) or specific (E) then depends on whether the observation is special.”

      That seems like it follows, but realize that it doesn’t have to. It’s mainly a distinction about whether we should take into account the fact that a universe is fine tuned vs an observer exists. E doesn’t have to be so specific; we could change it to simply read “some observers exist in a universe”. Which would still entail O, and from EP, we still get the conclusion that P doesn’t matter.

      I didn’t actually do the Bayes with the updated definition of E, but I’m pretty sure I’m right. Why? Because this Bayes’ analysis is equivalent to our ensemble analysis, and our ensemble is the ultimate way of expressing the selection effect and arguing that no observer is special.

      • Another dish-washing realisation…

        The notation for the posterior credence should just list all the givens.

        OK, sorry about the confusion. P(M) doesn’t mean the credence we should have for M, it means our prior naive credence. The posterior credence is just P(M|O&p=p1&N=whatever) etc. Gotcha.

      • I don’t really follow, I’m afraid. I don’t see a meaningful distinction between your “some observers exist in a universe” and my O, which is “there exists an observer-supporting universe”.

  19. DM,
    Yes, that’s exactly right, and the standard notation is just P(M) and P(M|O) for the prior and posterior.

    Now, I also realized something, actually in your model it seems P(O|M) is actually just 1, which is fine, it’s more like the IVF case, which is not a problem.

    And here’s the promised Bayes with E. You are right, E doesn’t contain any more relevant info than what I think you called E1, but I will call D = data = our universe exists and supports life. Let’s set p=1 for now. Then we have

    P(D|M) = 1 = N * P(D|S)
    P(M|D) : P(S|D) = Bayes factor * P(M) : P(S),
    where
    Bayes factor = P(D|M) / P(D|S) = N

    • Hi Dmitriy,

      > actually in your model it seems P(O|M) is actually just 1

      Yes, for p > 0 that’s correct.

      > P(D|M) = 1 = N * P(D|S)

      Yes, but this is starting to look “special”. P(1fad1449-a315-45ca-a685-da0aea33794e|M) = 1 = N * P(1fad1449-a315-45ca-a685-da0aea33794e|S), where M is generating every possible UUID and N is the number of possible UUIDs.

      So can you tell me why I shouldn’t use the above argument to assume that all possible UUIDs have been generated? Given that some universe had to be generated on S, what does D really tell us beyond O? Why is the fact that it was this universe and not some other significant?

      • To apologise in advance, here I’m just going to be flailing around a bit again because I don’t know how best to explain or generalise the problem I’m seeing.

        If you could help me by naming the fallacy in the UUID example above, it would be appreciated. It must be a named fallacy surely. Just because some event is wildly improbable doesn’t mean it is significant if it is drawn from a huge population of similar effectively interchangeable events.

        So, tentatively, I would propose that we shouldn’t replace O by D if D is interchangeable with a huge family of similar events. By interchangeable, I mean we could substitute it with any one of these without changing anything about the argument. I think you should add only relevant evidence, where relevant evidence actually affects the argument in some way. It is true that using D rather than O does affect the argument, but I mean that the specific details of D do not, so we should “generify” it to O, which is satisfied by any fine-tuned universe.

        But I also wanted to suggest that this really is the crux of the issue. Bayesian vs ensemble is a sideshow, as is everything else. It turns out that this is the very same thing that is the crux of the issue for many philosophers, including Philip Goff. It’s a point of active debate in the literature, I believe. So it’s an important point. I prefer the Bayesian argument to the ensemble argument because it surfaces it while the ensemble argument masks it.

      • Alex Popescu says

        Also, do you mean the inverse gamblers fallacy? And about the interchangeability; I don’t think that’s true precisely because it has to be this universe which is fine tuned. So if other universes are fine tuned, we can’t use that as evidence for D. It seems like O is interchangeable but D is not, no? Unless I have misunderstood you.

        But I fear we are just going to get stuck at an impasse regarding TER inevitably at this point. That’s why I prefer the ensemble (because it doesn’t actually argue that we are special). I don’t think the ensemble ‘masks’ the point of specialness. It stipulates by default that it’s only taking into account potential observers. Our universe being fine tuned at no point enters into it.

        It is tempting of course to think that because the ensemble and the Bayes analysis involving E reach the same conclusion, that they therefore must be based on the same premises. But I don’t think this is so; the Bayes’ solution (involving E) doesn’t actually take the selection effect into account. The ensemble is the only one that does this. Even your Bayes’ doesn’t do this because it argues that N is irrelevant to M being more preferable (which is contrary to the selection effect).

        So basically you are making arguments that are heavily based on appearances. It ‘appears’ the Bayes analysis is saying that we are special due to some weird identity issues; it ‘appears’ that the ensemble makes the claim that we are special etc… But these claims have to be actually demonstrated. In any case, I don’t think we’re going to make much progress at this point given that you insist on rejecting TER and don’t want to get into thread 2.

        Good luck with your moving process.

        Best,

        Alex

  20. Alex Popescu says

    Hey DM,

    Never mind that; I was just talking about our taking evidence into account. It is a vexing problem for me why it is so difficult to incorporate this selection effect into the Bayes’ analysis. I was naively hoping in my sleep deprived state that RMT could demonstrate some way why the Bayes’ analysis based on E is equivalent to our ensemble analysis. I totally understand why it seems like the Bayes’ analysis invoking E must somehow depend on our universe being special, but appearances are not the same as actual fact. In this case we have good Bayesian grounds to reject reasoning based on O (TER).

    So it seems that giving the Bayesian analysis involving E just reduces us back to debating TER; which I agree is unhelpful. That’s why I thought it might be more helpful to just talk in simple terms regarding your Bayes’ analysis contradicting our ensemble.

    Instead of debating TER, maybe you can tell us why your conclusion regarding your Bayes’, [that P modifies the odds ratio in your case, and that P modifies the naive credence for M (that discards the evidence based on E)]; should impact the credences for our ensemble?

    Because that’s what you are ultimately trying to prove no? My point is that the two conclusions are compatible, and so that means we have no reason to update the credences for the ensemble on the basis of your Bayes.

  21. Alex Popescu says

    I’ve been reflecting on the matter of the Bayesian and ensemble analysis being divergent regarding the ‘specialness’ of the evidence involved in the former but not latter. I think the fundamental problem here between the ensemble and our Bayes’ reasoning (involving E) is that the latter is observer relative. So Bayesian analysis is subjective to an individuals credences and knowledge, and their perspective entails these things. The ensemble on the other hand is simply making a claim about all potential observers. Where each potential observer is not more likely to experience M on account of P being more unlikely.

    The Bayesian analysis makes an additional assumption (that you are an observer). To even engage in such reasoning you have to assume that you are an observer in the first place, but the ensemble doesn’t require this. Thus by stipulating that we are an observer, the Bayes’ reasoning just demonstrates the ensembles’ claim that for any observer based in the ensemble, they can use E to reason to the ensemble’s conclusions.

    The trick here is to realize that the Bayesian reasoning based on O is actually masking things; it pretends to reason from a third person perspective when Bayesian reasoning is inherently first person. In other words, the evidence O (some universe exists) is applicable to any possible observer. But the problem is that by engaging in Bayes’ we are already stipulating that you are a specific observer.

    Therefore, by reasoning based on evidence that potentially applies to any observer you are failing to localize your evidence. Even though you have already localized your setting by engaging in such reasoning in the first place. Hence, it’s no surprise that O is no help for the Bayes’ reasoner to self-localize; given that they rely on evidence which is fundamentally non-local.

    The ensemble analysis on the other hand is the purest way of doing this, since it makes no stipulation about your having to be an observer, or about any such observers actually existing. Therefore it can appropriately use non-local evidence (some universes exist), because such evidence is specific to each observer. It’s the only such analysis that is capable of taking into account the selection effect at the appropriate level, because it is fundamentally a third person analysis.

  22. DM,
    I think you may have some misunderstanding about what *exactly* the lottery fallacy is, what the precise mathematical statement would be. I started writing a blog post about it because even Steven seems to misunderstand it.
    ***
    It’s never a fallacy to update on a stronger true statement (D instead of O). At worst the extra info is irrelevant, and then the posterior will be the same as when updating on the weaker statement.
    ***
    To your example,
    “””
    Yes, but this is starting to look “special”. P(1fad1449-a315-45ca-a685-da0aea33794e|M) = 1 = N * P(1fad1449-a315-45ca-a685-da0aea33794e|S), where M is generating every possible UUID and N is the number of possible UUIDs.

    So can you tell me why I shouldn’t use the above argument to assume that all possible UUIDs have been generated?
    “””
    Try to specify the an exact setup where that equation is actually true. If you can, in that example the evidence will provide support for M.

    • Hi Alex,

      Actually there were some points from you I didn’t address in my moderating comment.

      > So if other universes are fine tuned, we can’t use that as evidence for D. It seems like O is interchangeable but D is not, no?

      But had another fine-tuned universe been made actual on S, then observers in that fine-tuned universe could make the same argument. And anyone in M can make the same argument too. So the only reason D is special is because it’s our universe, which I think means we must hold ourselves to be special to regard D as special.

      > It stipulates by default that it’s only taking into account potential observers.

      I can see that we’ll need to move on to China/Chile arguments at some point. Thread 1 was productive but it seems it culminates in a well-rehearsed debate about TER and the lottery paradox, so perhaps the end of that thread is nigh.

      > because the ensemble and the Bayes analysis involving E reach the same conclusion, that they therefore must be based on the same premises. But I don’t think this is so

      Neither do I, really. Even if I’m wrong on TER and E is the right evidence to use, I prefer Bayes as it’s clearer. The ensemble argument seems too naive because it’s modeled on China/Chile [citation needed].

      > you insist on rejecting TER and don’t want to get into thread 2.

      The way I would put it is I’d like to understand why you don’t think the lottery paradox is a problem, and I’m deferring thread 2.

      • Alex Popescu says

        Hey DM,

        If you read my other reply; you’ll see that I wrote about the ‘specialness’ of D. Basically I argue that we need to know where D comes from; so that way we can deduce whether we are actually sneaking in some implicit claim (for the Bayes’ analysis based on D) that relies on the observer being ‘special’. I am putting special in quotes here, because I think your use of the word is actually equivocating from its normal usage in the lottery fallacy (I will get into this below).

        I argue in my other post above that just by engaging in Bayes’ reasoning we are already stipulating that we are a specific observer living in a specific universe. That’s because asking about credences is relative to a specific observer’s knowledge, which is dependent on their locality. For instance, an observer in another local universe couldn’t have access to the knowledge that our universe exists, in the way that we can.

        Why is this important? Because it means that there’s no specialness required to engage in Bayes’ based on D (or E). D is given by the stipulation that we are an observer; which is given by the fact that we are engaged in Bayes’ reasoning in the first place. Hence, it’s the other way around; there is no way to engage in Bayes’s reasoning while ignoring the fact that you are a specific observer with specific evidence (keep in mind every potential observer has access to their “special” evidence). So we don’t need to make special pleading on our behalf to believe that we need to argue from D, because such evidence is already given by our engaging in such reasoning.

        “The way I would put it is I’d like to understand why you don’t think the lottery paradox is a problem, and I’m deferring thread 2“

        Okay fair enough. I see that you’ve raised another latest objection (i.e. we are committing the lottery fallacy). I actually think Steven’s assertion about the lottery fallacy was the most confused point of all, and the weakest claim to be made regarding our reasoning. I’ve already talked about this in other places (and also RMT makes a brief point on this too above).

        But in brief, the lottery fallacy isn’t committed if we’re just updating our credences (which is what bayesian reasoning does). Rather, the lottery fallacy is invoked if you insist on there being an extra explanation for your being here outside the multiverse, without reason (this part is key). Notice it’s not enough to argue that we must assume that we are ‘special’ when we engage in justification (as Goff apparently does with his identity conditions).

        Firstly, I reject this thinking as previously mentioned; moreover, one only commits the lottery fallacy if one accepts that (if there was a multiverse) then (it would be an insufficient explanation for our being here purely on the grounds that we are special). But notice the latter isn’t used, even by Goff, to reject the multiverse (as an explanation of p). Why?

        Because the multiverse is rejected on the grounds that it needs to explain why our universe is fine tuned (which it doesn’t), and for which Goff gives reasons (e.g. TER). So the point is that if you have reasons for thinking that our universe must be explained; then you aren’t arguing that our specialness should protect us from the multiverses’ explanatory power. That’s because specialness is about arguing against something without invoking grounds, whereas we (including Goff) have grounds to reject the multiverses explanatory power (for our universe being fine tuned).

        It makes no sense to say that you’re committing the lottery fallacy if you reject A for reasons. The whole point of the lottery fallacy (and fallacies in general) is that you only commit it if you reject A for no good reason (i.e. because we are just “special”). This all stems from what I believe is a misreading of Goff by Novella. Novella I think was unfamiliar with Goff and White’s reasoning for the “this universe” objection. The reasoning was based on TER, but Novella didn’t appear to realize this (or address this).

        Also, I should clarify that when I say we are rejecting the multiverse’s explanatory power; I am just speaking of the relationship between the multiverse and fine tuning. I am NOT talking about whether the multiverse would or would not make a good explanation for cosmological conundrums; as was mentioned many times before, that’s a side discussion.

      • Alex Popescu says

        I wrote this:
        “ there is no way to engage in Bayes’s reasoning while ignoring the fact that you are a specific observer”

        But of course you can do so (that’s exactly what your Bayes’ analysis does). I meant to say that using Bayes’ reasoning that’s based on O, but not D, ignores the fact that we are specific observers. That’s bad because of what I wrote in my other post above (the 2nd last). Which is this:

        “ Therefore, by reasoning based on evidence that potentially applies to any observer you are failing to localize your evidence. Even though you have already localized your setting by engaging in such reasoning in the first place. Hence, it’s no surprise that O is no help for the Bayes’ reasoner to self-localize; given that they rely on evidence which is fundamentally non-local.“

        We are trying to self-localize when we ask whether we were more likely to be born in M or S

      • apopescu002@gmail.com says

        I should also mention that Goff doesn’t need to use the identity conditions justification for the “this universe objection”; he points it out because it’s an additional justification for D besides the TER principle. But if you think it makes our being here unnecessarily “special”, then feel free to discard it.

  23. Thanks Alex,

    As I think I may have addressed some of this in my comment that’s held up, I’ll wait until it shows up to see what else I need to say.

    In the meantime I’m working on something to explore the China/Chile issue, so I’m intending to return to thread 2 soon.

  24. Hi guys,

    Not sure if my missing comment is going to turn up. I’ll ask Philip to moderate tomorrow if not. Or retype it.

    In the meantime I’ve been working on a sharable online population simulator to interactively explore China/Chile vs Narnia/Lichtenstein vs M/S. I imagine I could express my point a lot quicker with text, but perhaps you’ll understand where I’m coming from more easily with the simulator. The simulator shows exactly how mutual exclusiveness should affect the ensemble argument. I show naive predictions for results (as works in China/Chile and doesn’t work in M/S) as well as more sophisticated predictions for the results that take any degree of mutual exclusion or compatibility into account, as well as actually simulating results with random trials.

    The results already show that the naive model will not work for M/S *given how I conceive of the problem* — all that remains is to format them for your viewing pleasure. These results are I suspect irrefutable, so I expect your reaction will be to dispute how I conceive of the problem.

    So we will be nowhere closer to agreement, but you should at least see how I conceive of the problem, which is worth something.

  25. DM, sounds fun!

    Does your missing comment including your thoughts on my defense of the Bayesian calculating based on D against your objection that using D instead of O commits the lottery fallacy? You gave an analogy with UUIDs, and I said if you make the situation precise then the objection will dissolve.

  26. Hi,

    I’m giving up on waiting for my comment to show up. Here’s an attempt to recreate it.

    Sorry if I’ve forgotten to respond to some points as I don’t remember exactly what’s already covered.

    RMT> I think you may have some misunderstanding about what *exactly* the lottery fallacy is, what the precise mathematical statement would be. I started writing a blog post about it because even Steven seems to misunderstand it.

    The link I gave before (not risking putting it in again for fear of moderation) describes what I’m thinking of. I don’t know how exactly to characterise the statement mathematically, but I think there are cases where there is clearly a mistake happening. I have illustrated such a case with the UUID. You haven’t responded with your reaction to the situation (i.e. how you would analyse it) so I’m not sure where to go from here.

    All you said was:

    RMT> Try to specify the an exact setup where that equation is actually true. If you can, in that example the evidence will provide support for M.

    So I’ll take *exactly* your argument but redefine the variables as follows:

    D = this specific UUID was generated by me today
    M = all possible UUIDs were generated by me today
    S = one UUID was generated by me today
    N = the number of possible UUIDs (2^122)

    P(D|M) = 1 = N * P(D|S)
    P(M|D) : P(S|D) = Bayes factor * P(M) : P(S),
    where
    Bayes factor = P(D|M) / P(D|S) = N

    So, unless I’m mistaken, by your logic if all you know is that one specific UUID was generated by me today, you should infer that all (or at least a decent fraction of) possible UUIDs have been generated by me today.

    That is to me obviously the wrong conclusion, so there’s something wrong with TER or how you’re using it. Tentatively, I think it’s that if we want to use more specific evidence it had better have something to do with the argument. If there is a class of interchangeable instances of evidence that would yield the exact same argument, then we should not talk about the probability of any specific instance but only of the probability of some member of the class.

    Alex> The trick here is to realize that the Bayesian reasoning based on O is actually masking things; it pretends to reason from a third person perspective when Bayesian reasoning is inherently first person.

    My Bayesian argument makes this step explicit when I move from O => E1. There’s a bit in there where I try to explain why. If TER is an issue for the argument, at least you can see where I’m making the mistake. But if I’m right about TER, and my assumptions about TER explain why the Bayesian argument is right, then the ensemble argument must be wrong. Yet there’s nothing about TER visible in the ensemble argument. But let’s get back to thread 2 when I’m ready to present the simulator.

    Alex> Hence, it’s no surprise that O is no help for the Bayes’ reasoner to self-localize

    I actually fundamentally disagree that this is a self-localisation problem. China/Chile is a self/localisation problem, because both exist, ex hypothesi. But M and S are mutually exclusive, so the question is only whether M exists or S exists, and the relative populations have nothing to do with it. This is just a statement of what I think, not an argument. I intend to follow up with an argument when the simulator is ready.

  27. More recent comments from Alex:

    > D is given by the stipulation that we are an observer; which is given by the fact that we are engaged in Bayes’ reasoning in the first place

    Right, but if a different world had existed in place of this one then some other observer would be making the same argument based on his D. In that sense, your D is not special. This is clear if you think about the ObserverCoin analogy. Each ObserverCoin essentially *is* an arbitrary UUID. But an ObserverCoin that reasons as RMT did would conclude that it should believe that all (or many) ObserverCoins should have been generated, which is the wrong conclusion.

    > Rather, the lottery fallacy is invoked if you insist on there being an extra explanation for your being here outside the multiverse, without reason (this part is key)

    Perhaps, but to me the only reason to so insist is if you think there is something very improbable about chance being the correct explanation. My point is that the Bayesian argument from D is making this same mistake. Yes, the chance of this specific D is low, but the chance of some D (i.e. O) is not, and that is all we need to account for D arising by chance. For this reason, we should work with O and not D, as demonstrated by the analogy to UUID or ObserverCoin.

  28. DM, this UUID example is very helpful. It is actually still underspecified in a subtle but critically important way.
    ****
    So I’ll take *exactly* your argument but redefine the variables as follows:

    D = this specific UUID [***RMT: say 15285944…, let’s call it X***] was generated by me today
    M = all possible UUIDs were generated by me today
    S = one UUID [***random***] was generated by me today
    N = the number of possible UUIDs (2^122)

    P(D|M) = 1 = N * P(D|S) [***true, but only under the specification that the definition of D is: D is defined as true if and only if X was generated at some point today
    The exact specification is CRITICALLY important here, so I want to ask you – is that what you want D to be? It’s your example so use a different definition of D if that’s not the one intended***]
    P(M|D) : P(S|D) = Bayes factor * P(M) : P(S),
    where
    Bayes factor = P(D|M) / P(D|S) = N

    • Hi Dmitriy,

      > is that what you want D to be? It’s your example so use a different definition of D if that’s not the one intended

      Yes, with reservations, because I don’t see the distinction you’re drawing. As far as I can see there’s no difference between your proposal for D and mine. So if it becomes clearer when you actually present your argument, it’s possible I will backtrack and say that no actually I disagree with your D.

      Assuming that X means “this specific UUID”, as you suggest.

      I said D means that X was generated by me today.
      You said that D is defined as true if and only if X was generated at some point today.

      I said “means that” and you said “defined as true if and only if”. These are synonymous to me (I think). I guess “means that” could be taken to be synonymous with “implies” and “defined as true if and only if” is “equivalent”. So the difference would be that on the weaker “implies” interpretation, D could be false even if X were generated today. I did not intend for this interpretation. I intend “D” and “X was generated by me today” to be synonymous, equivalent expressions.

      I included “by me” and you did not. The idea behind “by me” was just to make the intuition that the conclusion is wrong stronger — it’s imaginable that there are lots of people generating UUIDs today somewhere. But I know that it’s crazy to assume that I personally did.

      You included “at some point” and I did not — I don’t think this is doing any work so it can be ignored.

      • apopescu002 says

        DM,

        I think RMT means that x is defined to be a specific number. So by agreeing to that; it would be equivalent to specifying in advance that you’ll be surprised if this number x comes up, and then it goes ahead and comes up.

        Also, I’m not sure that I agree with RMT that if the condition ‘D iff X is specific’ is met then we are justified in inferring a large M. That’s because it seems like there is no selection effect at play here (unless I missed some part of the analysis). Perhaps RMT thought that this was a condition of your UUID generation.

        Here’s three different scenarios:
        a) if you specify that the UUID is going to be a certain number, and it ends up generating that number today (in a small subset). Which of course is wildly improbable. Then you can demand an explanation (i.e. generator is rigged), but you can’t infer M (inverse gamblers fallacy).
        B) You didn’t specify a number (no D iff x is special condition). And the UUID spits out a random number; then you can’t infer anything.
        C)There is a selection effect, you are put to sleep and will only wake up iff UUID spits out a certain number. You wake up; you can infer you need an explanation, but you can’t infer M from the degree of P (this universe objection). Rather, it’s based on your prior for M and N.

        I assume you are using scenario A. Notice then that it doesn’t follow that N increases the probability of M being the case. Why? Because M doesn’t increase the chance of the specific UUID being generated in a particular instance, or a subset of generations outside of the additional ones that M stipulates. Though it does increase the chance that the same UUID will be generated in the set of all numbers generated.

        Without a selection effect, you’re not going to notice the past numbers generated that match your specific UUID; so they’re irrelevant.

      • Alex Popescu says

        Just ignore that comment (I wrote a follow up below). I wrote it almost two days ago but it had trouble going through moderation. I didn’t realize then that M was specifically defined to be instantiated in the same time frame that D can possibly take place; that’s how RMT does it. The time frame is key to implement the selection effect properly in my opinion.

  29. Ok, perfect, yes I am glad you clarified that you didn’t mean just “implies”. Then the calculation is correct.
    ****
    So, unless I’m mistaken, by your logic if all you know is that one specific UUID was generated by me today, you should infer that all (or at least a decent fraction of) possible UUIDs have been generated by me today.

    That is to me obviously the wrong conclusion,
    ****
    The conclusion then is not wrong, and in fact I think intuitively obviously correct.

  30. This might be an important subtlety. I used “D is true iff..”, but of course if some statement is true but I think it’s false, then Bayes will fail, so the hopefully obvious precondition is that the the agent knows D if and only if D is true.

    • > so the hopefully obvious precondition is that the the agent knows D if and only if D is true.

      We don’t need that precondition.

      We can just say that the Bayesian argument is applicable iff the agent’s beliefs about D correspond to D. We don’t require any logical necessity that the two correspond. So I don’t think your skeptical objection (e.g. that I might be dishonest) is on point at all.

      • Although to be fair that may just be what you mean about it being a precondition.

        But I think this goes without saying. The same would go for any syllogism.

        If I tell you that Socrates is a man, and that all men are mortal, then normally I think you would agree with me that you can conclude that Socrates is mortal.

        More generally, how could you ever know for sure that all men are mortal or even that Socrates is a man? This is like worrying about my dishonesty, I feel. Whatever the evidence you take to warrant your premises (like me telling you I generated a UUID), your assumptions could nonetheless be mistaken. You don’t need to stipulate the assumption that your assumptions must be true — because then you’d need to stipulate that that new assumption is true etc ad nauseam. It’s understood that an argument is only applicable if its premises are true, so even if you could conduct a misleading Bayesian analysis on false information, I don’t think that this matters.

        This question about whether I’m honest has nothing to do with this particular problem as far as I can tell.

  31. So if I tell you that just now I generated the UUID 66543102-5024-4cad-80c8-e2484fd12561, do you in fact believe that I probably generated every single possible UUID?

    No, because it hasn’t been specified what the connection is between D being true and you telling me D. If you could be lying I obviously can’t do normal Bayes, right? What if you are “selectively honest”, meaning if you tell me D then D, but maybe you only tell me D if you generated just one UUID, otherwise say nothing or give me some other information? Then again normal Bayes doesn’t apply, not until the situation is specified correctly.

    • This seems really evasive.

      I did in fact generate it, because that is a UUID. I either generated it with a tool or I made it up by hand or had someone else generate it on my behalf, or I picked it from a pre existing list — I think we can interpret all of these scenarios as various ways I could have generated it. Validate it however you like — that is a UUID, and beyond any radical skeptical doubts like “Maybe I’m dreaming” or whatever, I think you should believe I generated a UUID. And so you should believe that D. And so you should assume that D is true in your reasoning.

      You’re so out on a limb here, I feel, that you might want to consider backing down an admitting that there’s some problem even if you can’t account for it.

      I wonder what Alex thinks?

    • > but maybe you only tell me D if you generated just one UUID, otherwise say nothing or give me some other information?

      I think we can assume by stipulation that I’m honest, so I don’t think this issue arises.

      However I do now see a problem with my argument. If I generate all possible UUIDs, then I have to select one to show you. If you are picking all the evidence according to TER, then you should pick D = “X was generated by DM and selected to show me”. The probability of this does in fact not rise with M, because generating more UUIDs does not increase the chance of me showing you that specific UUID.

      I’m not sure yet if there’s a way around this, but I would offer two points.

      If O is “Some UUID was generated by DM”, and P is “X was generated by DM”, and Q is “X was generated by DM and selected to show me”, then it’s a bit odd that our credence by M goes up and then back down again as we go from more generic to more specific. That doesn’t prove anything, it’s just odd.

      Secondly, the problem disappears if we think about the ObserverCoin example. From the ObserverCoin’s perspective, there is no selection other than the selection effect of the observer. I still think it’s obvious that the ObserverCoin would be wrong to assume M, but I suspect you will disagree.

    • I think the conclusion follows from the calculation and the conclusion as applied to this scenario is the wrong conclusion. So this is the wrong calculation. I think that this demonstrates that there is a problem with how you are using (or abusing) TER.

  32. I don’t quite understand how your position has shifted now. On the one hand you say
    “””
    However I do now see a problem with my argument. If I generate all possible UUIDs, then I have to select one to show you.
    “””
    which seems to suggest you now see my point that without the precondition “agent knows D iff D” normal Bayes would be obviously inapplicable. Do you?

    But on the other hand you say
    “””
    > but maybe you only tell me D if you generated just one UUID, otherwise say nothing or give me some other information?
    I think we can assume by stipulation that I’m honest, so I don’t think this issue arises.
    “””
    Honesty only means if you tell me D, then I can know D. But that’s only one direction, if you say nothing sometimes when D is true you’re not lying, but it’s no longer true that I can if D then agent, me, knows D.

    Basically if the problem doesn’t specify in which cases I do and don’t get certain info, then it’s not a problem of honesty, it’s just a lack of specification, which would obviously make the calculation impossible.

    We can talk about the observercoin too, but do you now agree that your example, once made precise, doesn’t show that my calculation commits the lottery fallacy or gives a wrong answer? I don’t mean to say we proved there is no error in my calculation, only that your objection based on that specific uuid example, doesn’t go through? If so we can tackle another objection.

    • My position hasn’t shifted at all really. I only realised that the UUID analogy is not a perfect analogy to M vs S. The inference from the Bayesian analysis on “D = this specific UUID [***RMT: say 15285944…, let’s call it X***] was generated by me today” is still incorrect, thought the argument is valid. The problem is that I realised that the move is open to you to say that it is only incorrect because we didn’t include *all* the information — specifically we did not include the information that on M I must have selected X from the list of all the UUIDs I generated.

      So I stand by what I said:

      “I think the conclusion follows from the calculation and the conclusion as applied to this scenario is the wrong conclusion. So this is the wrong calculation.”

      But the problem for me is that you could argue that it is the wrong calculation because it is not specific enough, whereas I want to say that it is the wrong calculation because we were too specific.

      The ObserverCoin analogy is better.

      > which seems to suggest you now see my point that without the precondition “agent knows D iff D” normal Bayes would be obviously inapplicable. Do you?

      No, this is a separate problem. On the problem I raise, there is no worry about honesty or “agent knows D iff D”.

      I agree that it helps to clarify the circumstances under which you know what. But that is easily done and doesn’t affect the argument, as far as I can see.

      Suppose we agree beforehand that I will either generate one UUID or a bajillion UUIDs, and that I will then tell you one of the UUIDs I generated. And suppose I’m honest. Your issue is then dealt with.

      But mine is not. There doesn’t need to be a mismatch between “agent knows D” and “D” for my issue to arise. Because if I generate a bajillion UUIDs, I still must somehow select that specific UUID from the list to show it to you, and that remains as improbable as generating only X in the first place. So it is not true that P(D|M) > P(D|S) if we interpret D as including the knowledge that we have agreed that I should tell you of only one UUID.

      > We can talk about the observercoin too, but do you now agree that your example, once made precise, doesn’t show that my calculation commits the lottery fallacy or gives a wrong answer?

      I agree that there are problems with this example because of the worry I raised. But it is still the case that the calculation applied to UUID does indeed commit the lottery fallacy. The problem is that this does not invalidate TER, because this calculation while fallacious does not use all the evidence, and what I’m trying to show is that there’s something wrong with TER.

      ObserverCoin on the other hand does use all the evidence (I think) and so does invalidate TER. ObserverCoin is more analogous to M vs S because it has the same observer selection effect. Both appear to me to commit the lottery fallacy just like the UUID example while following TER.

      • Alex Popescu says

        Hey DM,

        Sorry I’ve been having some difficulties with my WordPress account as of late (as you can see by my posts under different names: apopescu002). Hopefully this comment goes through. I think the selection effect is key here. If you are stipulating that M is the hypothesis that all possible numbers were generated in the same time period as D was required to occur (i.e. today); then you are taking into account the selection effect.

        So, basically if D is specified to take place only today, then I would have noticed any X (where X satisfies D) that took place (I would have noticed any such weird number being generated today) if M was true. But if the numbers generated in the set of M were instead specified to happen in the past (or at some undetermined time), then we would be committing the inverse gambler’s fallacy to argue for M. That’s because stipulating possible events in the past don’t explain present events. Meaning that I wouldn’t have noticed the X’s being generated by M if they happened before today.

        So this all depends on whether the events of M and the set of all possible observed events coincide (or overlap in time). Dmitriy has defined this scenario so that the answer is yes; in which case I agree that M becomes more likely in proportion to N.

  33. “””
    Suppose we agree beforehand that I will either generate one UUID or a bajillion UUIDs, and that I will then tell you one of the UUIDs I generated. And suppose I’m honest. Your issue is then dealt with.

    But mine is not. There doesn’t need to be a mismatch between “agent knows D” and “D” for my issue to arise. Because if I generate a bajillion UUIDs, I still must somehow select that specific UUID from the list to show it to you, and that remains as improbable as generating only X in the first place. So it is not true that P(D|M) > P(D|S) if we interpret D as including the knowledge that we have agreed that I should tell you of only one UUID.
    “””
    So you are saying that even after you specify the situation precisely, alleviating the problem with “agent knows D iff D”, my calculation is still committing an error. If that turned out to be true then I think my analysis of the multiverse falls. We would not even need to analyze other analogies, like observercoin.

    But there is no error, the lottery fallacy in particular is not committed. Recall
    ***
    P(D|M) = 1 = N * P(D|S) [***true, but only under the specification that the definition of D is: D is defined as true if and only if X was generated at some point today
    The exact specification is CRITICALLY important here, so I want to ask you – is that what you want D to be? It’s your example so use a different definition of D if that’s not the one intended***]
    ***
    You have now changed the specification, and consequently, as I said in that quote, P(D|M) = 1 = N * P(D|S) is no longer true. So where is my error?

    • Let us agree right now to the terms of an experiment we could actually do.

      I’m not going to generate all possible UUIDs because that is infeasible. But let’s say I’ll either generate one random number from 1-100 or I’ll generate all numbers from 1-100.

      Let’s say the probability of each case is 50%. I flip a coin to decide what to do, in effect.

      After I have generated my number(s), I choose one and tell you what it is. You must then choose whether you think I generated one number or 100 on the evidence of whichever number X I give you.

      D = I generated X
      M = I generated 100 numbers
      S = I generated 1 number
      O = I generated some number
      N = 100
      P(D|S) = 0.01
      P(D|M) = N * P(D|S) = 1
      P(O|M) = 1
      P(O|S) = 1

      You know D iff D

      I think that meets all your requirements for an argument that should be analogous to your multiverse argument, and I think it’s clearly wrong. Following your multiverse argument, you should conclude with 99% confidence that I generated 100 numbers when in fact your confidence should clearly be 50%.

      If you are in any doubt as to this, we could run the experiment a few times. I promise to be honest. Or you can be the coin flipper and you promise to be honest.

      But there is still my problem. We need to consider ObserverCoin instead because though your argument about UUID is wrong, it doesn’t prove you’re wrong about M vs S. Because if you wanted to be more specific, you could define D as “I generated X and selected it to show Dmitriy”. You are entitled to do so because you think we have an obligation to consider all the relevant evidence. Now it would no longer be true that P(D|M) = N * P(D|S) = 1. In fact P(D|M) would be just the same as P(D|S), assuming I choose from the generated list in a uniform manner.

    • > You have now changed the specification, and consequently, as I said in that quote, P(D|M) = 1 = N * P(D|S) is no longer true. So where is my error?

      This doesn’t seem right. I didn’t change the specification. My intention was always “You know D iff D”, I think that can be assumed in all syllogisms. I don’t think that “You know D iff D” changes anything about P(D|M) = 1 = N * P(D|S) if D is defined as true if and only if X was generated at some point today.

      • Are we talking at cross purposes?

        Under the terms of the experiment, you only ever get to see one number.

        “You know D iff D” should not be interpreted to mean that if I generate 100 numbers, you know I generated 100 numbers. You only know I generated one number, and so D is only defined relative to the particular number X I show you. X is a constant, not a variable, denoting whichever value I show you, not any value I generate.

    • To make it even more concrete, and I don’t know if WordPress will allow this, but let’s say I have just run the following program:

      var N = 100;
      var S = Math.random() < 0.5;
      
      if (S) {
          // S - print one of the numbers at random
          console.log(parseInt(Math.floor(Math.random() * N + 1)));
      } else {
          // M - print all the numbers
          for (var i = 1; i <= N ; i ++) {
              console.log(i);
          }
      }
      

      I don’t know if you can read Javascript but it’s just the program I described above.

      I am now going to run the program once, right after finishing this sentence, and I will be bound by the results.

      I report that the number 34 was printed to console. What are your credences about how many numbers were printed to console and why?

  34. That is a fine change, from uuids to numbers. But the problem is there are two possible specifications that give different answers. The one from before was equivalent to:
    1. D = “27 has been generated”; and you will tell me if D obtains or not.
    In that case P(D|M) = 1 = N * P(D|S)

    The new specification, or perhaps the one you actually had in mind all along (even though we specified X = [some specific uuid] = basically 27, do you agree that doing that makes it spec.1?), is

    2. Let D(X) = “X has been generated”; and you are not saying that for any X I will know D(X) iff D(X) of course. You are saying you will pick X at random among the ones generated and tell me D(X) for that one X.

    So if you now tell me “36 was generated” I now have to properly set up the calculation. If I were to let D = D(36), the precondition “agent knows D iff D” will not be fulfilled. So I let D = D(36) AND “36 was selected randomly by DM to be told to me”. Now the precondition is obviously fulfilled and I can apply Bayes theorem to update on my evidence. I hope you know what the result will be, without me needing to write it out:) No wrong result, no inconsistency, do you agree?

    • Hi Dmitriy,

      I only ever thought as X as a convenient label for “the single number I tell you about” and D as “X has been generated” — you’ll note that I started off using actual values and you introduced the X as a convenience, so I don’t see this as a change. You appear to have thought of X as having a universal quantifier in front of it or something. In particular I interpreted as “agent knows D iff D” to mean that you will know that the specific number I tell you about has been generated iff the specific number I tell you about has been generated. This is all true in the experiment as I laid it out.

      But it’s good we’re on the same page. This is the advantage of code, perhaps. Coding something by necessity removes any ambiguity.

      > No wrong result, no inconsistency, do you agree?

      Agreed. The change you have made to add “36 was selected randomly by DM to be told to me” is exactly what I was getting at. This means that this is not analogous to M vs S by my lights. Which is why we should move to ObserverCoin. The only difference here being that your perspective is necessarily limited to observing only X because your identity is bound up with it. If X were otherwise, you wouldn’t be you. Just as if this universe were otherwise, you wouldn’t be you, and just as if the ObserverCoin, identified by its UUID, wouldn’t be that particular ObserverCoin if its UUID were different.

  35. Ok, I think we are closer to being on the same page. I remember that you had a specific value and I introduced X. But note that specifying a specific value in advance is what happens in spec.1, not spec.2.

    So are we now agreed that no lottery fallacy or any other error happens in the calculations for the uuid example, regardless of the specification?

    • Hi Dmitriy,

      We are on the same page. In particular, I want to apologise for thinking you were out on a limb, and for not recognising what you were getting at earlier.

      The lottery fallacy would (I think) apply to the uuid example if you picked the intermediate definition of D as “X has been generated” but not at the most generic “Some number has been generated” or the most specific “X has been generated and selected for presentation to me”.

      But my brain is fried so I don’t know.

      Looking forward to seeing how you think of the ObserverCoin example which doesn’t have an analog of “and selected for presentation to me”, or at least that’s the idea.

  36. And I agree with you about the advantage of code, by which I think you mean specifying the setup super precisely. So if we are on the same page with uuids, we can do the same with observercoins, and then maybe with IVF etc.

    • The problem with those is you have to identify with a perspective in the simulation. Code-wise, it’s pretty much the same as what I already gave you. You just have to imagine that “console.log” means a new perspective is born which is identified by the number, and then ask what should be believed from that perspective if all it knows is the source code and its own number. I guess another way to put it is that each of the 100 observers we’re considering only knows anything at all if their number is selected.

      • We could maybe do something like this in real life, but we’d need 100 unwitting participants, and each participant would only get to know that they were participating in the experiment at all when I informed them that their allocated number had been chosen. So it’s not very practical but it is imaginable. What should such a participant believe on being informed of the setup?

        Now, when I put it like that, if I’m honest, I have to say my intuitions go along with yours. Each participant should bet there were lots of participants, because each participant is special to him/herself at the time of the experiment, and it is surprising to be chosen.

        But if the experiment brings them into existence then I don’t share your intuition, because at the time of the experiment, there is no observer to whom the participant’s ID is special. The very existence of the perspective is contingent on the improbable event, so that perspective should not be surprised by the improbable event.

        I guess I can see in any case how you may just stick to your guns with ObserverCoin and say that each ObserverCoin should believe M to be true from its perspective. I think that’s wrong, but it’s hard to prove. If so, then at this point it may be best to agree to differ and move onto the problems I perceive with the ensemble argument (unless you think I’m crazy to interpret ObserverCoin differently and you want to explore my absurd intuitions).

  37. Ok, I think I understand the setup. I hope 🙂
    To convince you of the right answer (the coin should assign 100:1 to M:S), can I propose a slightly different scenario first to see if we are on the same page there? I think it will really help.

    S1. One coin generated. Then with probability 50% letter M is put in a file scenario.txt, otherwise letter S is put in. Coin can’t see this file. Then, if S, coin is destroyed with probability d= 1-q, where q = 1/N = 1/100, otherwise nothing happens to it. Coin doesn’t know if it survived because of M, or because of S + luck.

    If coin survives, what odds should it assign to M : S?

    • M is 0.5 probability. S + luck is 0.5 * 0.01 = 0.005 probability.

      Odds are 0.5 : 0.005 or 100 : 1 for M : S.

      I can see what you’re driving at, obviously. Clearly I can’t say that ObserverCoin is different from UUID just because of the temporal ordering of events when M vs S is decided — since your coin doesn’t know when M or S was decided it could have been any time.

      I want to say that the point is that there exists a perspective for your ObserverCoin when it is anticipating and trying to predict the outcome. Your ObserverCoin can be in a place where it can be unsure as to its survival, and I think something of this epistemic state carries over even after the event. Before the event, it can assess what it should believe if it survives, and it’s committed to stick to those beliefs. It’s particular survival to it is special in the way that rolling 6,6,6,6,6,6,6 is special — it has the potential to be surprising and to demand explanation.

      But as soon as the perspective for my ObserverCoin exists, the outcome is already decided. It can see that there’s nothing particularly special about its survival, as somebody had to survive. It seems more like rolling 5,4,2,5,5,6,2. My ObserverCoin can only exist in the first place if it is going to survive. I think that matters and I’m guessing you don’t. I’m not sure I can convincingly justify it though. I can try to come up with arguments perhaps, but it will just be more tentative flailing around unless I have an insight. It just seems obvious to me that ObserverCoins should not predict M only on the basis that they exist, and that causes me to be cautious about adopting TER.

      Are we at an impasse or is there some way forward on thread 1?

  38. There might be. Because I have a couple of cute modifications to my scenario. First, all coins are created in a sleeping state, they are only woken up if they survive. Second, now suppose first 100 coins are created , each with a unique id. Then M or S is chosen as before, and if S 99 random coins are destroyed. What about now, what should an awakened coin assign to M:S?

  39. Hi Dmitriy.

    Interesting. I think if a coin is created but it is sleeping until after M vs S is decided, I’m inclined to say this is equivalent to it not being created until M vs S is decided.

    So I’m inclined to analyse this taking O as my evidence — some coin exists, so it’s 1:1 M:S

  40. Hey DM,
    I think that view has a very high intellectual price tag. What if the coin is first conscious for a millisecond, and then put to sleep? Does it matter if it knows the whole setup before it’s put to sleep? What if it’s created in a conscious but immature, child-like state?

    You would have to draw the line somewhere, it’s not clear to me how you would do that. And of course my and Alex’s view is completely immune to these conundrums.

    • I can understand your view.

      I don’t think it necessarily has to be a strict cutoff or phase transition from one state to another. To the extent that you identify with an earlier self you can recall before the cull, then you should be surprised to have been lucky (and increase your credence in M). To the extent that you can’t, you shouldn’t be surprised.

      I accept that this is a high intellectual price tag and not very satisfying.

      I should note again that this whole time I’ve been trying to argue as if I am not a modal realist (MUH). But as I think modal realism is more or less necessarily true, in actual fact fine tuning does not increase my credence for a multiverse much, as that credence is already near 100%. So perhaps I’m not the best person to defend the view. It might be worth reading some of the responses to White’s paper.

      In any case, I understand why you don’t find the Bayesian argument compelling or to defeat the ensemble, even if I’m not convinced that the matter is settled. Should we move on to the problems I see with the ensemble argument?

      • I wonder what you make of the discussion of Fred the uranium atom and related points on page 8 of this paper? Are these points you’ve already addressed or do you think they’re new to the discussion? It seems persuasive to me, as and the suggestion that we can use more generic evidence as long as the specific evidence doesn’t disconfirm seems plausible.

        Click to access This%20Universe.pdf

      • One other point, on the fuzziness or unsatisfyingness of my view. This thought is not well developed, it’s just an instinctive reaction. Maybe it’s wrong.

        You could maybe try to investigate which way of modelling this is right with something like your ensemble argument, and see which way of predicting works better.

        But to do so you would have to make a judgement call on what the reference class of the ObserverCoin is. Is it just some coin or is it a coin with this specific id? Or maybe an observer from the class of possible experiments of this nature? Or a generic observer of any sort? Depending on what you assume, you might get different answers. I think this parallels the problem with the Bayesian analysis — you have to make a judgement call on whether you deem yourself to be just some observer or an instance of a specific kind of observer or specifically you.

        This kind of fuzziness may be unavoidable.

      • Alex Popescu says

        “This kind of fuzziness may be unavoidable.“

        I wouldn’t say it is unavoidable; since we have methods for determining which types of evidence are better than others. I think TER is quite a reasonable assertion. It’s almost self evident in a way that the analysis which takes the most evidence into account is best.

        I want to illustrate this to hopefully make this feel more intuitive. For example, I could reason that on the basis of the fact that I am a living creature; it is more likely than not that I am capable of photosynthesis (since the total plant biomass dwarfs the total animal biomass). What has gone wrong here? What has gone wrong is that we have disrespected TER.

        I do know that I am a loving creature, but I also know that I am an animal (more specifically a human being). Call this evidence A. And call the living creature evidence L. A entails L, so according to TER we should take the conclusions of A over the conclusions of L, and this perfectly comports with common sense.

        About reference class:
        The point about the reference class is interesting, because both the Bayes’ analysis using D and our ensemble presuppose that we belong to the most general class. That is, we could have been born in any possible universe in M or S. That’s because we are interested in taking into account the selection effect, and then showing that even if you do so it nevertheless follows that P doesn’t modify our credences for M.

        The Bayesian analysis using O on the other hand doesn’t entail that we are in the most general reference class (where every conscious observer is treated equally). You could stipulate by default that the observer in your Bayesian analysis (and we could actually see this more easily if we did an ensemble just based on O) could have been born in M or S, AND that they belong to the most general reference class. But if you do so then you will have to argue that the M in your Bayes is a special type of M; for example it only produces one fine tuned universe etc…

        Why? Because making the second stipulation (that we should use the most general reference class) is equivalent to saying that the observer was equally likely to have been born in any fine tuned universe in M. But that also entails that N matters (at all scales), regarding the odds of the observer being born in M. This is contrary to your analysis, where N makes less and less of an impact in proportion to its size (because M only needs to guarantee a single fine tuned universe).

        So, to get away with both stipulations, you would have to say that M is special. On the other hand, if you want a normal multiverse, then you have to make some special considerations for the observer (he/she no longer belongs to the most general reference class). The point is that we are trying to tell you that (either through Bayes or an ensemble), relying on an analysis that disrespects TER/uses weaker evidence actually entails that you have to change the reference class for the observer in question (so we are no longer taking into account the selection effect).

        A key point:
        Above all, I think you are missing a crucial distinction which is this. We are concerned with the Relationship between which categories of evidence belong to which categories of hypothesis. Whereas you are just treating the entire category of evidence that is particular as being weak, and the entire category of evidence that is general as being strong. But that isn’t the correct way of going things at all.

        Rather, it’s actually the case that if we are trying to prove a particular hypothesis (am I more likely than not to be a plant?) then I should particular evidence (I am an animal). But if I am trying to prove a general hypothesis (are most living things plants or animals) then I should use general evidence (the ratio of plant biomass vs animal biomass on earth).

        It’s this proper relationship which is the key to the correct way of doing things. In this case, if you are using Bayesian analysis, then you are stipulating by default that you are a particular observer. Also, it doesn’t matter that you could have been an entirely different observer. What matters is that all possible Bayesian reasoners must be particular observers, and all possible Bayesian reasoners must therefore have access to particular evidence (their universe is fine tuned).

        The only way to do a general form of reasoning is to use an ensemble analysis. That is because the ensemble analysis doesn’t stipulate that you must be a particular observer, and it can therefore ask the appropriate general question (what is the ratio of potential observers in M vs S?). Therefore we need to use general evidence in our ensemble (which of course we do).

        I hope all this has been helpful for giving you an intuitive sense of why we need to respect TER; as well as a clearer sense for why I think that if we are doing Bayes then we need to use particular evidence.

        Also, you are free to argue of course that we shouldn’t say that we belong in the most general class (and that we are actually special observers). I’m not going to get into that because our analysis was all about just showing that if you accept that there is a selection effect (like Steven does); then it follows that P doesn’t modify our credences in M.

      • Alex Popescu says

        I wrote that “I am a loving creature”

        I meant to say that “I am a living creature”.

        I’m not so sure about the former. 🙂

  41. (Sorry for the big gap linking to a PDF seems to have created on the page)

    Hi Alex,

    I’ve seen your comments that got through moderation just now.

    In light of how the conversation has moved on, and in how I acknowledged that the UUID scenario doesn’t show what I want it to show, they probably don’t need a response any more, do they?

    • Alex Popescu says

      I completely agree; although I did just post a new comment on why I think you’re missing a crucial aspect in your focus on our need to adopt a general class of evidence (O) as opposed to a particular class (D). You say we need to do this to avoid invoking ‘specialness’, but I argue that is the opposite and I show why.

    • Alex Popescu says

      Also, I didn’t read the paper in its entirety, but about the “this planet’ objection, I would say that of course such an objection is not sound. Why is it not analogous then to the ‘this universe’ objection? The answer is quite easy; we already know that there exist other planets, in more than enough sufficient quantity to explain why our planet is compatible with life. Whereas this is not at all the case in the multiverse. But suppose that it were; suppose that we knew that there existed a multiverse powered by inflation. Then of course it follows that we can no longer reason to the ‘this universe’ objection.

      Why? Because now we have an independent line of evidence for M, so TER no longer holds. That’s because before, the only way to deduce O was through D. Whereas now we can deduce O from M, which is based on evidence independent from D (whatever it was that made us so sure in M).

      So we are not saying that the multiverse, if true, doesn’t explain our perceiving a fine tuned universe (or why we exist). It most certainly does.

      Best,

      Alex

      • Alex Popescu says

        I have read further into the paper. The part about Fred and the atom violates the principle that I spoke of above, regarding how we should appropriately categorize classes of evidence and hypotheses.

        So this: “We leave the oracle in a room with the sample and come back an hour later. The oracle tells us that just one uranium atom decayed: Fred.
        From the fact that Fred decayed we deduce that one uranium atom decayed. Can we proceed to use half-life calculations to estimate the number of uranium atoms in the sample? Not if we are required to reason from the fact that Fred decayed rather than the fact that some uranium atom or other decayed”

        is certainly true. But the authors make the same confused conflation that I argue you have made, which is that TER is not about saying that the class of particular evidence is always stronger than the general class. In the example of Fred, since we aren’t trying to determine the particular likelihood that Fred would have been born, but rather the general likelihood of uranium atoms decaying, we shouldn’t reason on the basis of Fred. So TER is not disrespected here because we aren’t trying to come to the conclusion of how likely the individual decayed atom was to have been born in one sample over another. In that case, I would argue that we couldn’t reason to a bigger sample (suppose that we already knew there was at least a 1 kilogram sample, just as we already know that there is at least S) on the basis of decay being very unlikely in a 1 kilogram sample, for the reasons mentioned.

        So the bottom line is that the total evidence principle is all about talking into account all the total relevant evidence. For a general claim, particular evidence isn’t relevant, whilst for a particular claim, general evidence is too non-specific. Is Fred’s existence relevant here? Absolutely not, if the oracle had just told us that some particle decayed then we could have reasoned to the same conclusion.

        What about in the multiverse claim, is the fact of the observer’s specific universe being fine tuned relevant to their deriving O? Of course it is, if the observer’s universe wasn’t fine tuned then they couldn’t be alive, and they most certainly would not have derived O. Whereas, in our hypothetical setup, the only way to have derived the existence of some particle decaying was from the oracle; which is independent of knowing that there is a specific particle that is fine tuned (she doesn’t have to tell you the latter). So in the latter scenario it’s possible to get ‘some particle decayed’ without knowing that your particle decayed. In our M case, it’s not possible to get that some universe is fine tuned without knowing that your specific universe is fine tuned (this holds true for all observers) UNLESS you have strong independent lines of evidence for M, which we assume that we don’t in our case.

        All of this leads to the interesting result that we can actually dispute the Bayesian analysis in the hypothetical instance that we have good solid evidence/grounds for M. And this is where mine and Dmitriy’s criticisms relating to Goff come into consideration. By relying on the particular that is the Bayesian analysis, Goff is conflating the two issues of ‘P being evidence for M’ and “M being a reasonable belief’. The Bayesian analysis relies on the latter being false, in order to demonstrate the former. The problem with this is that the two things are independent, as the ensemble shows.

        It’s also important to point out that the Bayesian analysis doesn’t actually entail that the two things are dependent; that’s because our concluding that the Bayesian analysis is wrong on the basis of our knowing M, only means that you can’t derive “p doesn’t affect M’ from TER at that stage. However, it doesn’t then follow that the claim “p doesn’t affect M” is refuted, because we can still demonstrate it through other means. This is why the ensemble is so important in the end.

        Best,

        Alex

      • Alex Popescu says

        By possible, I mean that there is no logical contradiction between “not being possible to derive the name, because of the oracle not telling you the name of the particle” and “the oracle telling us that some particle decayed”. Whereas, there is a logical contradiction between knowing “some universe is fine tuned” and “not being possible to derive our universe is fine tuned”. Because for every observer, it holds true that the latter being the case means that they necessarily can’t derive that some universe is fine tuned. Barring absurd hypotheticals like an observer teleporting from another universe.

  42. Hi Alex,

    > I wouldn’t say it is unavoidable; since we have methods for determining which types of evidence are better than others.

    But how you apply those methods depends on how you conceive of the problem, which is partially perhaps an issue of how you conceive of your personal identity. I’m not sure they settle the question.

    > What has gone wrong is that we have disrespected TER.

    Both I and the paper I linked to suggested some ways we might want to add caveats to TER. I agree that we should respect TER where those caveats do not apply. However they do apply in your example. I suggested that we should use specific evidence if it has a bearing on the argument we want to use (as opposed to some other interchangeable member of the generic class). The paper suggested we are obliged to use specific evidence if it disconfirms the original argument. That you are a human as opposed to a plant does change the argument, so my caveat applies. That you are a human as opposed to a plant disconfirms the hypothesis, so the paper’s caveat applies.

    > because both the Bayes’ analysis using D and our ensemble presuppose that we belong to the most general class.

    It’s not obvious to me (although I may be missing something) that reasoning from D puts you in the most general reference class. It might put you in the reference class of observers with evidence D. To me, perhaps naively, reasoning from O seems to be a broader reference class.

    > Why? Because making the second stipulation (that we should use the most general reference class) is equivalent to saying that the observer was equally likely to have been born in any fine tuned universe in M.

    You’ve lost me, I’m afraid. I’m not following your argument, but I have the sense it’s not a core issue right now. Or is it?

    > Whereas you are just treating the entire category of evidence that is particular as being weak, and the entire category of evidence that is general as being strong.

    I don’t think so. I just think it matters as to whether the specifics of the particular evidence have a bearing on the case. Again, the UUID analogy fails, I agree, but in this case I think it is easier to get to the right answer by reasoning from the premise that *some* UUID has been generated rather than that this *particular* UUID has been generated. So there are some cases where the particulars are irrelevant and are best ignored. The “Fred the uranium atom” discussion from the paper I linked may be a better example, as it’s not immediately obvious to me that it suffers from the same issue as the UUID analogy.

    • Alex Popescu says

      I agree it’s not obvious that reasoning from D puts you in the most general reference class. You really should read that latter half of my post, which it appears you may have partially skipped over, to understand why I think that. And also to understand my objections to the Fred argument.

    • Alex Popescu says

      In particular this part:

      “Rather, it’s actually the case that if we are trying to prove a particular hypothesis (am I more likely than not to be a plant?) then I should particular evidence (I am an animal). But if I am trying to prove a general hypothesis (are most living things plants or animals) then I should use general evidence (the ratio of plant biomass vs animal biomass on earth).

      It’s this proper relationship which is the key to the correct way of doing things. In this case, if you are using Bayesian analysis, then you are stipulating by default that you are a particular observer. Also, it doesn’t matter that you could have been an entirely different observer. What matters is that all possible Bayesian reasoners must be particular observers, and all possible Bayesian reasoners must therefore have access to particular evidence (their universe is fine tuned).”

      • Alex Popescu says

        Finally, I want to retract this claim: “And this is where mine and Dmitriy’s criticisms relating to Goff come into consideration. By relying on the particular that is the Bayesian analysis, Goff is conflating the two issues of ‘P being evidence for M’ and “M being a reasonable belief’. The Bayesian analysis relies on the latter being false, in order to demonstrate the former”

        It was wrong of me to say such a thing on Dmitriy’s behalf. Whether you feel this way is going to depend on your interpretation of TER. One interpretation is that it’s applicable to all cases of relevant reasoning based on evidence that is entailed by another piece of evidence. Another interpretation is that TER should only be used if we don’t have independent grounds for deriving that weaker evidence in question (in our case O). I need to reflect some more on this issue to say how I feel about it (whether the first interpretation can work).

        In any case, it’s tangential to what we are taking about. Don’t worry about it because it’s quite a complicated topic and I don’t think I have the communication skill to do it justice. If I change my mind on this issue however, I will issue a retraction so as not to needlessly accuse Goff of making a mistake.

  43. Hi Alex,

    I probably won’t have time to give your comments the attention they deserve today.

    I just wanted to make one quick note.

    I suspect the problems we are discussing are related to the sleeping beauty problem (Google it if you don’t know it — I’m afraid of links now). This problem has been contentious for quite a while and there is no consensus solution.

    I’m not going to try to draw the connection as I don’t have time. But if there is a connection, it indicates to me that it is not so easy to establish which way of thinking is correct. Possibly there is no fact of the matter. Possibly we’re in a situation like geometry where we can accept the parallel postulate or not and arrive at different geometries (or in this case, different decision theories).

    Anyway, as we’re now debating points well-rehearsed in the literature, I feel we should all agree that my Bayesian argument is contentious, i.e. not straightforwardly right or wrong. That means that it is also contentious whether the ensemble argument’s conclusion is right. But from a superficial reading of the argument it seems straightforward, and it’s not clear how it could be contentious. I think this is a problem with the ensemble argument because it’s misleading.

    • Alex Popescu says

      The reason my posts where so long is because I attempted to comprehensively lay out the case for why:
      1) The ensemble doesn’t have to rely on us knowing that our universe is fine tuned for its soundness, but the Bayesian analysis does.
      2) Constructing a Bayesian analysis that relies on O but not D, counterintuitively requires that the observer is special in some way (provided M is a normal multiverse).
      3) TER may initially seem like it’s counterintuitive, but actually the approach which respects TER is the one that accords the best with our intuitions.
      4) We need to categorize appropriate relevant evidence with the appropriate relevant hypotheses. Once we have done so we can see that all Bayes’ reasoning that fails to incorporate D is fundamentally incapable of self-localizing (that’s because all Bayesian reasoners must be particular observers).

      Therefore, I think 4 shows that using only O must be the wrong approach. And that’s going to be true even if you object on grounds like “we couldn’t have possibly been born in other worlds”, as you long as you stipulate that’s not a consequence of our being special. And really regardless of any such objections you can raise (again as long as you don’t require that the observer is special).

      Consequently, forgive me if I think that I’ve conclusively shown why your Bayes’ approach must be flawed, and furthermore that the Bayesian approach using D is the only legitimate approach to answering the question. I admit I am not the best communicator and I must work on that aspect, but hopefully it’s clear enough.

      Of course I agree that this is controversial, that’s the whole point of why we are bothering to give reasons for why we are right. If it wasn’t controversial then we wouldn’t have to bother with such reasoning in the first place no?

      That said, if at some later date you wish to get into my analysis and have concerns/questions, then I’d be happy to address them. But if not, I believe I’ve made my case and so will be withdrawing from the thread for the time being.

  44. Hi Alex and DM,

    I thought the site broke because I could only see DM’s comment for a second before it would disappear but now I understand what happened.Anyway, the Fred atom story has an easy resolution showing it doesn’t lead to any problems to use the specific rather than general evidence. I put this in the form of a blog post: https://www.reasonmethis.com/2021/03/an-atom-named-fred.html

    I am surprised seasoned philosophers who wrote that article thought that their example is evidence against TER.

    My position, briefly, is that:
    it can never lead to an error to use all evidence, I believe no situation could ever be produced that would lead to an error if all evidence is used. The worst thing that can happen I claim is that part of the evidence is just irrelevant and doesn’t affect the answer.

    – the Bayesian analysis always gives identical results to the ensemble analysis, as long as the same evidence A is used.

    • Alex Popescu says

      Hey RMT,

      I agree with your analysis. However, I think there is some confusion here regarding how we should interpret the author’s claim. Briefly, in White’s article, D is interpreted as no evidence for M on the grounds that M doesn’t explain why this universe is fine tuned. So when White says “Reasoning from D does not work to confirm M” he means that M is not a good explanation for D.

      Similarly, analogously the authors here are just saying that “if reasoning from the fact that Fred exists is not evidence for the half life calculations working” that’s because “the half life calculations being correct don’t explain why Fred (this particular atom) decayed when he did”.

      I don’t believe that they would object to your pointing out that using M or S will still entail (rightly) different results on account of our using F, upon the correct input (N). Or that we do get a different probabilistic calculation by using F, but this equally applies to both M and S.

      Rather, I think they are saying that using evidence F (Fred exists) doesn’t help us to reason to the fact that a certain half life calculation is correct (S) in this narrow instance of backwards probabilistic inference. That’s because in such cases, reasoning based on F just means trying to show that S is more likely than M, because S better confirms F.

      I gather that the authors are saying that the half life calculations pertaining to S are correct, but we couldn’t use them provided that we thought they needed to explain why Fred exists.

      For if we add on the extra condition that Fred has to exist, then assuming Fred, on average, could be expected to pop into existence every time period T (which roughly corresponds to the time observed); it follows that our half life calculations that we would derive are way too optimistic. We would basically come to the wrong conclusion that there must be a huge uranium sample (M).

      In other words, the authors are contending that in some narrow cases of backwards probabilistic inference (BPI), they believe TER fails, because relying on all the evidence in some cases can result in us needlessly adopting extra conditions which are irrelevant and harmful. And that’s because BPI is about showing that hypothesis H is more probable on account of it being the best which can account for evidence E.

      In this case, relying on evidence E just means using it to set up the stipulated conditions that hypothesis H must take into account. This latter part is key.

      I think the authors are ‘technically’ right here, provided we interpret the TER principle too literally. However, we can easily get around this by introducing the extra stipulation that TER is all about taking into account *relevant evidence. Since Fred’s extra condition is irrelevant, we shouldn’t take it into account. So I consider TER to be a principle which concerns itself with all the *relevant total available evidence; whereas they interpreted it as being just about all available evidence.

      I wonder if you agree with me here.

      • Alex Popescu says

        And of course in this case we know S is more likely to be correct, because there weren’t a huge number of uranium atoms which decayed prior to Fred popping into existence. I do agree in the end that their interpretation (taking non-relevant evidence into account) is way too literal and rather silly though.

        I actually think the paper in its entirety had rather weak objections beside this (like the this planet objection). No offense intended to the authors.

      • Alex Popescu says

        To be fair, TER is supposed to be all about helping us distinguish which piece of evidence is relevant or not. The point about the Fred case being obviously non-relevant is to help us realize that this isn’t always going to be the case. Because this isn’t clear in the example of the ‘this universe’ objection. However, again I think the rebuttal here is clear; which is that we shouldn’t be using TER in a vacuum.

        TER must be combined with other methods if we want to correctly distinguish relevant from non-relevant evidence. And I came up with such a method in my earlier posts (I adopt a method for how to appropriately sort categories of evidence in relation to categories of hypotheses). TER just deals with one aspect of relevancy; which is that having to do with logical entailment.

      • Alex Popescu says

        Also I’ve made a trivial mistake here, I wrote:
        “ We would basically come to the wrong conclusion that there must be a huge uranium sample”

        I meant to say, we would basically come to the wrong conclusion that the half life calculations must be different (decay is drastically faster) for a given sample, S.

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