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.

298 Comments

  1. Hey Alex, there are several passages in your account that I didn’t follow. Could you formulate, maybe in mathematical notation, what mistake would be made in using all available information, not just the relevant bit? In my post I seem to have shown that the credences of S and M would be updated correctly either way. So I don’t see what possible mistake can occur then. If you can formulate this mistake in the same notation I use in the post, we could maybe add it to the post.

    • Alex Popescu says

      You’re absolutely right; I missed that part. But that’s not a problem for their general objection; just a problem for their example. I offered a “steel man” version of their argument which shows that if we reason on the basis of Fred, then the half-life calculation must be different. That’s pretty easy to follow I think.

      If Fred, then likelihood of Fred happening is 1/N more times unlikely than a random uranium atom decaying. But we just know that one uranium atom decayed; therefore it is wrong to use the extra condition that the uranium atom has to be Fred. So the point is that you are right that, as stated, their argument fails. But we can give a better version of the argument which shows that we shouldn’t rely on the extra condition stipulated by reasoning on the particular (Fred) in all cases. Even if the particular entails the general.

      • Alex Popescu says

        Hey Dmitriy,

        I think we’ve both screwed up our interpretations. 🙂

        I’m pretty sure that the authors are just saying that reasoning on the basis of Fred “blocks” us from inferring a hypothesis here, meaning that we have no reason to prefer M over S, or the other way around. Because of course, M doesn’t make Fred happening more likely than S (as you showed). Whereas, in reality, knowing that one atom decayed, we do have a reason to prefer one or the other (i.e. if the average decay time is longer, then S more likely). So, by showing that the S and M calculations are the same; you’ve inadvertently confirmed their point. It’s confusing, but in any case my example is fully compatible with their point as well.

    • Alex Popescu says

      I should have said, “what you actually showed”; as opposed to “what you meant to show”. Although I suppose that sounds way too arrogant 🙂
      So I agree that your derived equation is correct; we just disagree on the correct interpretation of N. And also, I think the interpretation is anyway irrelevant to demonstrating the author’s more general point. For the prospective reader; check out Reason Me This’ link where I lay out my argument in the comment section (it’s a small section) as to why I think Reason Me This (and DM moreover) are both wrong.

  2. “If Fred, then likelihood of Fred happening is 1/N more times unlikely than a random uranium atom decaying. But we just know that one uranium atom decayed; therefore it is wrong to use the extra condition that the uranium atom has to be Fred.”
    But the calculation in my blog post shows how incorporating the extra condition simply doesn’t change the Bayes factor, and therefore is not wrong. This would happen just the same in your example.

    ” But we can give a better version of the argument which shows that we shouldn’t rely on the extra condition stipulated by reasoning on the particular (Fred) in all cases. Even if the particular entails the general.” I agree, if you interpret that as saying there is no need to rely on the extra condition. I would not agree if you meant doing that would mess up the answer.

  3. Hi Alex,

    > 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.

    I can’t follow the logic of the remainder of this comment as it pertains to reference classes (I have read it) because you seem to be talking about something different to me or reasoning from assumptions I don’t share. It seems to me that reasoning from D is putting the agent in the reference class of “people who have observed this specific universe to exist” and reasoning from O is putting the agent in the reference class “people who have observed a fine tuned universe to exist” and the latter is more general than the former. I don’t mean to add some extra stipulation that the agent is in the most general reference class, as you say I do. I just mean the reference class is implied by the form of the argument itself.

    > [You should read} 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?)

    I did. I addressed this. It’s not a good example because it violates the caveats I suggested and the “Fred” paper suggested. I said “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.”

    > That is because the ensemble analysis doesn’t stipulate that you must be a particular observer

    I think the ensemble analysis may make assumptions about reference class by how it constructs its populations. Different analyses with different assumptions could therefore yield different answers, just as with Bayesian analysis reasoning from D or from O. But this idea is half-baked and there are other points I would want to make agains the ensemble analysis.

    > 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.

    I’ve seen this point made a few times, in Goff’s paper as well I think. I must confess I haven’t really internalised it. I still find it hard to see how I could believe the multiverse to explain the mystery of fine tuning, while at the same time believing that the mystery of fine tuning is not any kind of evidence for the multiverse. Is there a quick and easy example to demonstrate how A can explain B while B gives no reason at all to increase credence in A even a smidgeon? If we didn’t know of other planets and other solar systems, it seems to me that the “fine-tuning” of earth would give reason to believe in other planets and other solar systems. That’s what I take the “This Planet” analogy to be talking about. However it is true that the rhetorical purpose of the analogy is that we do in fact know the answer for this case even if we don’t for “This Universe”, so it helps to push intuitions in my direction, perhaps unfairly.

    > we shouldn’t reason on the basis of Fred

    TER as given by White just says we should use all the evidence we can bring to bear. That means that according to TER, it is a fallacy to reason about “some” atom when we could reason about Fred specifically. The criterion you are introducing may be an improvement on TER (it’s similar to the caveats I want to introduce), but if we adopt your criterion we then open a can of worms about what is the appropriate framing of the question we are trying to ask about the multiverse. That is something we can argue about and debate (and we’re doing just that), so we no longer have a golden rule like TER to settle the matter. The Fred example demonstrates that TER cannot be applied mindlessly and uncritically and that’s all it needs to show.

    To me, the question the multiverse hypothesis is answering is not “Why is this specific universe fine-tuned?” but “Why is an actual universe fine-tuned?”, because I don’t take the specific indexical features of this universe (e.g. it contains me) to be significant. The former question feels to me like asking about Fred.

    But this is debatable, certainly! That’s my point.

    > 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.

    Of course it isn’t, if the observer’s universe wasn’t fine tuned (but some other universe was), then some other observer would be alive, and they most certainly could have derived O.

    > To be fair, TER is supposed to be all about helping us distinguish which piece of evidence is relevant or not.

    I don’t see anything like this in White’s original proposal. Goff defines TER as ‘…in the confirming of hypotheses, we cannot, as a general rule, set aside a specific piece of evidence in favor of a weaker piece.’

    There’s nothing there about distinguishing what is relevant. That’s your own addition.

    White’s original proposal seems to be just asserting that specific evidence is always to be preferred to general evidence, at least where relevant. It doesn’t tell us how to tell if it’s relevant. My understanding is that using irrelevant information is fine because it shouldn’t affect the result (that’s what makes it irrelevant). The fact that reasoning from this specific universe gives a different answer than reasoning from some generic universe is just what makes it relevant. But the same thing goes for Fred.

    • Alex Popescu says

      “I did. I addressed this. It’s not a good example because it violates the caveats I suggested and the “Fred” paper suggested. I said “That you are a human as opposed to a plant does change the argument,”

      With all respect I don’t think you understood my point there. I wasn’t arguing that it doesn’t change the argument if you use some class of evidence, nor saying that it is wrong to use the general class of evidence. I was giving criteria for how we should properly categorize such things, which the Fred objection falls afoul of.

      So I’m not sure what you meant by saying that it is not a good example, because I wasn’t defending us having to rely on any piece of evidence in that quote; rather I was saying that we have to rely on such particular evidence IF we are trying to prove/demonstrate a particular claim.

      “I think the ensemble analysis may make assumptions about reference class by how it constructs its populations.“

      Of course, I meant that our ensemble doesn’t make such a stipulation; which is however required for all Bayesian reasoners (a point I noticed that you did not address).

      “I don’t see anything like this in White’s original proposal…
      There’s nothing there about distinguishing what is relevant. That’s your own addition.”

      We are just saying the same thing here. Distinguishing relevant from non-relevant evidence just means telling us which piece of evidence is applicable or not. TER tells us that D is applicable but not O, therefore it is helping to distinguish relevant from non-relevant evidence. My point is that this principle is incomplete however, which leads on to my next.

      “The criterion you are introducing may be an improvement on TER (it’s similar to the caveats I want to introduce), but if we adopt your criterion we then open a can of worms”

      Yes and no. I am introducing some criterion (which is really quite intuitive and common sense I argue), but notice I’m not saying that we have to modify TER. That’s because I take the TER definition to be saying that we should reason on A over B, if A entails B, ceteris paribus.

      The latter part is key; I think TER is simply incomplete, not wrong. As mentioned, it’s just one ways of determining relevancy. So I argue that where the Fred objection runs afoul is in it being not relevant, but we have to determine it’s irrelevancy through other means (which as mentioned, I think are easy to see). Therefore, I disagree that we are modifying the TER principle in any way that would have implications for the multiverse argument.

      “Of course it isn’t, if the observer’s universe wasn’t fine tuned (but some other universe was), then some other observer would be alive, and they most certainly could have derived O.”

      Note that the phrase: “the observer’s universe” is an indexical one. So my claim still holds true regardless of your objections that some other observers could be alive etc… the point is that engaging in Bayesian analysis entails that there must be an observer somewhere. And it is a true statement that every observer could not have been alive if their universe wasn’t fine tuned. Therefore, we see that my conditions for relevancy are in fact met by D.

    • Alex Popescu says

      Hey DM,

      I wanted to clear up this:

      “I still find it hard to see how I could believe the multiverse to explain the mystery of fine tuning, while at the same time believing that the mystery of fine tuning is not any kind of evidence for the multiverse. Is there a quick and easy example to demonstrate how A can explain B while B gives no reason at all to increase credence in A even a smidgeon?”

      Because I agree that it can seem a confusing thing to possibly believe on our part. When I wrote “if the multiverse were true, it explains fine tuning” I meant exactly that, no more and no less. Notice I’m not saying that the multiverse, if true, explains the fact that our particular universe is fine tuned (it doesn’t). So we don’t actually have to believe that “A can explain B while B gives no reason at all to increase credence in A even a smidgeon”.

      Rather, I am saying that if the multiverse were true, then the “this universe” objection doesn’t hold. That’s because I am arguing that in this case TER would no longer hold (remember how I said that I thought TER was incomplete? This is an instance of that). Therefore, it follows that we should adopt the “some universe” line of reasoning (because we can derive O from M), which would explain fine tuning (why we are here). And of course I’ve always believed that M does explain why some universe is fine tuned, and that knowing (just) that some universe is fine tuned should increase our credence for M, so long as TER doesn’t hold of course. Hopefully this makes things clearer.

  4. Hey,

    I don’t really want to discuss TER any more. Too many tangents, too many points to address, too little time.

    I’m left with the feeling that TER as applied to the multiverse is contentious in much the same way as the sleeping beauty problem. We’re not going to get to the bottom of it.

    Incidentally, on the Sleeping Beauty problem, I’m a halfer but I suspect from your arguments that you guys would be thirders, is that right?

    So I think that’s it for thread 1 for me.

    I intend to revisit this at some point and focus on what I think is wrong with the ensemble argument. But I want to get back to my simulation first so I may need some time, even if all that remains are presentational issues.

  5. Alan MacRobert says

    Nope. What the Joker-didn’t-kill-you thought experiment misses is that it assumes from the outset that the thought experiment is not happening in a multiverse, but happens just once. So of course the “conclusion” proves the assumption.

    A true analogy would be to consider that scenario might be playing out many times in a multiverse — just like we wonder whether our real world is. In other words, what if a very number of these setups exist: Jokers, typing monkeys, and yous. Each of the yous, of course, thinks he’s the only one. The vast majority of them are killed in their sleep and never come to consciousness to see what the monkey improbably typed. But a very rare one will — and the you that sees this happening must be one of those.

    If fact, if you did wake up in that situation, positing a multiverse of Jokers, typing monkeys, and yous would be a complete and sufficient explanation of the extraordinary fact of what the monkey typed.

    I’m surprised that a philosopher didn’t recognize committing such a basic logical fallacy. You can “disprove” anything by postulating from the outset that the thing is not true and then building your proof logically from that.

    I suspect a common thing philosophers do: overlooking self-selection. In other words, assuming that there is “obviously” only one you, with no possibility of copies of you in a multiverse who, of course, also think they’re the only one. TBH, philosophy is rather known in academia for its high population of egotists — an assumption of “I’m the center of things, there’s no one like me” — who might thus have an especially hard time grasping the slippery implications of anthropic self-selection effects, both large and small.

    Alan MacRobert

  6. Alan MacRobert says

    Typo fixes:
    “consider that scenario” ==> “consider that that scenario”
    “very number” ==> “very large number”

  7. The question I’m addressing is whether the fine-tuning gives you evidence for a multiverse. Your analogy assumes a multiverse and explores the implications. I agree if we start from the assumption that there is a multiverse, then our evidential situation changes. But my question is what grounds do we have to take that possibility seriously. Are you suggesting finding ourselves in the Joker scenario, or finding a monkey typing English, would give us grounds for believing in a multiverse? You’re going to quickly lose evidential support for any non-multiverse hypothesis if every extraordinary event entails a multiverse. Not even multiverse theorists think that. Also, when. you study philosophy, you get taught about this: https://en.wikipedia.org/wiki/Ad_hominem

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