In passing, I said:

From a statistical standpoint, lottery winners don't exist - you would never encounter one in your lifetime, if it weren't for the selective reporting.

And lo, CronoDAS said:

Well... one of my grandmothers' neighbors, whose son I played with as a child, did indeed win the lottery. (AFAIK, it was a relatively modest jackpot, but he did win!)

To which I replied:

Well, yes, some of the modest jackpots are statistically almost possible, in the sense that on a large enough web forum, someone else's grandmother's neighbor will have won it. Just not your own grandmother's neighbor.

Sorry about your statistical anomalatude, CronoDAS - it had to happen to someone, just not me.

There's a certain resemblance here - though not an actual analogy - to the strange position your friend ends up in, after you test the Quantum Theory of Immortality.

For those unfamiliar with QTI, it's a simple simultaneous test of many-worlds plus a particular interpretation of anthropic observer-selection effects:  You put a gun to your head and wire up the trigger to a quantum coinflipper.  After flipping a million coins, if the gun still hasn't gone off, you can be pretty sure of the simultaneous truth of MWI+QTI.

But what is your watching friend supposed to think?  Though his predicament is perfectly predictable to you - that is, you expected before starting the experiment to see his confusion - from his perspective it is just a pure 100% unexplained miracle.  What you have reason to believe and what he has reason to believe would now seem separated by an uncrossable gap, which no amount of explanation can bridge.  This is the main plausible exception I know to Aumann's Agreement Theorem.

Pity those poor folk who actually win the lottery!  If the hypothesis "this world is a holodeck" is normatively assigned a calibrated confidence well above 10-8, the lottery winner now has incommunicable good reason to believe they are in a holodeck.  (I.e. to believe that the universe is such that most conscious observers observe ridiculously improbable positive events.)

It's a sad situation to be in - but don't worry: it will always happen to someone else, not you.

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So with what probability should Barack Obama believe he is on a holodeck, and how should this belief influence his behavior?

And not only Obama. The closer you are to the center of human history, the more likely you are to be on a holodeck. People simulating others should be more likely to simulate people in historically interesting times, and people simulating themselves for fun and blocking their memory should be more likely to simulate themselves as close to interesting events as possible.

And...if Singularity theory is true, the Singularity will be the most interesting and important event in all human history. Now, all of us are suspiciously close to the Singularity, with a suspiciously large ability to influence its course. Even I, a not-too-involved person who's just donated a few hundred dollars to SIAI and gets to sit here talking to the SIAI leadership each night, am probably within the top millionth of humans who have ever lived in terms of Singularity "proximity".

And Michael Vassar and Eliezer are so close to the theorized center of human history that they should assume they're holodecking with probability ~1.

After all, which is more likely from their perspective - that they're one of the dozen or so people most responsible for creating the Singularity and ensuring Friendly AI, or that they're some posthuman history buff who wanted to know what being the guy who led the Singularity Institute was like?

(the alternate explanation, of course, is that we're all on the completely wrong track and that we're simply in the larger percentage of humans who think they're extremely important.)


Still, I think that in most EU calculations, the weight of "holy crap this is improbable, how am I actually this important?" on the one side, and of "well, if I am this dude, I'd really better not @#$% this up" on the other should more or less scale together. I don't think I'm stepping into Pascalian territory here.

And Michael Vassar and Eliezer are so close to the theorized center of human history that they should assume they're holodecking with probability ~1.

The "with probability ~1" part is wrong, AFAICT. I'm confused about how to think about anthropics, and everybody I've talked to is also confused as far as I've noticed. Given this confusion, we can perhaps obtain simulation-probabilities by estimating the odds that our best-guess means of calculating anthropic probabilities is reliable, and then obtaining an estimate that we’re in a holodeck conditional on our anthropic calculation methods being correct. But it would be foolish to assign more than, say, a 90% estimate to “our best-guess means of calculating anthropic probabilities is basically correct”, unless someone has a better analysis of such methods than I’d expect.

Shouldn't the fact that they can probably imagine better versions of themselves reduce this probability? If you're in a holodeck, in addition to putting yourself at the center of the Singularity, why wouldn't you also give yourself the looks of Brad Pitt and the wealth of Bill Gates?

We are actually in a 'chip-punk' version of the past in which silicon based computers became available all the way back in the late 20th century. The original Eliezer made friendly AI with vacuum tubes.

The more powerful computers are when you turn 15, the higher the difficulty level.
8Scott Alexander
1. No if they are in a historical simulation. The real architects of the Singularity weren't billionaires. 2. No if they are in some kind of holo-game, for the same reason that people playing computer games don't hack them to make their character level infinity and impervious to bullets. Where would be the fun in that?
Not really. Think of Nozick's experience machine. If you were to use the machine to simulate yourself in a situation extremely close to the center of the singularity, would you also give yourself the looks of Brad Pitt and the wealth of Bill Gates? a) Would this not make the experience feel so 'unreal' that your simulated self would have trouble believing it's not a simulation, and therefore not enjoy the simulation at all? In constructing the simulation, you need to define how many positive attributes you can give your simulated self before it realizes that its situation is so improbable that it must be a simulation. I'd use caution and not make my simulated self too 'lucky.' b) More importantly, you may believe that a) doesn't apply, and that your simulated self would take the blue pill, and willingly choose to continue to live in the simulation. Even then, having great looks and great wealth would probably distract you from creating the singularity. All I'd care about is the singularity, and I'd design the simulation so that I have a comfortable, not too distracting life that would allow me to focus maximally on the singularity, and nothing else.
I agree these are possibilities. However, it seems to me that if you're going to use improbable good fortune in some areas as evidence for being in a holodeck, it only makes sense to use misfortune (or at least lack of optimization, or below-averageness) in other areas as evidence against it. It doesn't sit well with me to write off every shortcoming as an intentional contrivance to make the simulation more "real" for you, or to give you additional challenges. Of course, we're only talking a priori probability here; if, say, Eliezer directly catalyzed the Singularity and found himself historically renowned, the odds would have to go way up.
The alternate explanation is of course far more likely a priori.
1Eliezer Yudkowsky
How likely is it that, say, at least 10 people think they're Barack Obama, only one of which is correct?
Being mistaken about your importance is different from, and much more common than, being mistaken about who/where you are.
4Eliezer Yudkowsky
Unless most conscious observers are ancestor simulations of people in positions of historical importance, in which case most people are correct about the importance of the position and incorrect about who/where they are. (Vide Doomsday Argument, Simulation Argument, and the "surprise" of finding yourself on Ancient Earth rather than much later in a civilization's development. Of course these are all long-standing controversies in anthropics, I'm just raising their existence.) Among people who believe themselves to be Barack Obama, most are mistaken about their position rather than the importance of the position.
Not all that unlikely. There have certainly been a lot of people who have believed themselves to be Napoleon or Jesus. I'd say 10 Obamas seems a little right now, but I wouldn't be at all surprised by, say, three.
"seems a little MUCH right now", I meant.
The idea of eternal inflation might cut against this. Under eternal inflation new universes are always being created at an exponentially increasing rate so there are always far more young than old universes. So under this theory if you are uncertain of whether you are at a relatively early (pre-singularity) or relatively late (post-singularity) point in the universe you are almost certainly in the relatively early state because there are so many more universes in this state. Note: Eliezer and Robin object to this idea for reasons I don't understand.
James, I don't think inflation implies there are more early than late universes, nor do I object to inflation. I just don't think inflation solves time-asymmetry.
Note that the alternate explanation is MUCH more probable.

I don't think it should influence his behavior very much. Even if he assigns strong probability to being in a holodeck, his expected utility calculations should, I think, be dominated by the case in which he is in fact PotUS, since a president is in a better position to purchase utility.

I think The Onion has this one covered.

So if you find you ARE that friend, presumably you'd have no fear of stepping in front of that gun barrel yourself for a few million flips right afterwards. I mean it's pretty convincing proof. Then you get to see the confusion in each other's face!

Though you're both more likely to end up mopping your friend's blood of the floor.

On the whole, I think a good friend probably doesn't let a friend test the Quantum Theory of Immortality.


Even if QTI is true, a good friend doesn't test it, for fear of leaving behind (many copies of) a bereaved friend.

I don't believe so. While the person who underwent the experiment has a completely convincing proof of MWI+QTI, the friend doesn't. What he saw is just as unlikely under MWI as it is under Copenhagen.
If you didn't believe in MWI+QTI (i.e. had very low priors for), and you saw your friend claim to do a billion coin flips and not get shot, then even if you "refuse" to significantly increase your belief in MWI+QTI, wouldn't you at least increase your belief in the possibility that the gun is broken, and thus would not shoot you?
I would assume that the gun was broken and thus would not shoot me.

Although it was not via the lottery, my wife's sister won one million dollars on a TV show in the 1980s called "The one million dollar chance of a lifetime". It turns out that she and her husband would get $40,000 a year for 25 years, but they got divorced a few years later, so she received $20,000 a year until recently. It was quite a contrast between the show's promise to "make you a millionaire" and the actual very modest improvement in lifestyle from an extra $20,000 a year.

Anyway, none of you know her so this doesn't disprove the ... (read more)

I get the feeling that there must be an "anthropic weirdness" literature out there that I don't know about. I don't know how else to explain why no one else is reacting to these paradoxes in the way that seems to me to be obvious. But perhaps my reaction would be quickly dismissed as naïve by those who have thought more about this.

The "obvious" reaction seems to me to be this:

The winner of the lottery, or Barack Obama for that matter, has no more evidence that he or she is in a holodeck than anyone else has.

Take the lottery winner. W... (read more)

The idea of a holodeck is that it's a simulated reality centred around you. In fact, many, most, or all of the simulated people in the holodeck may not be conscious observers at all.

So, either I am one of 6 billion conscious people on Earth, or I am the centre of some relatively tiny simulation. Winning the lottery seems like evidence for the latter, because if I am in a holodeck, interesting things are more likely to happen to me.

As you say, when someone wins the lottery, all 6 billion people on Earth get the same information. But that's assuming they're real in the first place, and so seems to beg the question.

I'm not yet seeing that other peoples' consciousness per se is relevant here. All that matters is that there be a vast pool of potential winners, conscious or otherwise. All that I (the winner, say) observed was that one of the members of this pool won. If my prior belief had been that every member of the pool had an equal probability of winning, then I have no new evidence for the holodeck hypothesis after I observe my winning as opposed to any other member's. I would have predicted in advance that some member of the pool would win that week, and that's what I saw. However, I take your point to be that it would not be rational to suppose that there were millions and millions of potential winners, each with an equal chance of winning. So, I now concede that initially there is a certain asymmetry between the lottery winner and a non-winner: The non-winner initially has stronger evidence that he or she was among the pool of potential winners, and that the odds of winning were distributed evenly throughout that pool. Of course, the winner has strong evidence for this, too. But I agree that the non-winner's evidence is initially even stronger. However, I disagree that these respective bodies of evidence are incommunicable, as Eliezer claimed. If I, the winner, observe you, the non-winner, sufficiently closely, then I will eventually have as much evidence as you have that you were a potential winner who had the same chance that I had. (And if it matters, I will eventually have as much evidence as you have that you are conscious. I side with Dennett in denying you an in-principle privileged access to your own consciousness.)
In the event that you win, you gain the information that a conscious person has won the lottery. When someone else wins, you merely gain the information that a "person" who may or may not be conscious has "won the lottery". The holodeck hypothesis predicts that interesting events are more likely to happen to conscious persons. Since you know that you are conscious, if you receive more than your fair share of interesting events, this seems to be (rather weak, but still real) evidence for the holodeck hypothesis. For as long as you are studying me, yes. And then afterwards I get deleted and what you see of me is again just a few lines in an algorithm using up a couple of CPU cycles every hour. (This post brought to you by universe.c, line 22,454,398,462,203)
Heh, true. But I confront the same possibility with regards to my observation of my own consciousness.
0Paul Crowley
You believe in p-zombies?
No. But the simulation doesn't need to run perfect simulations of humans who aren't currently the focus of the, uh, holodeck customer's attention.
You are missing something, and would benefit greatly from reading Nick Bostrom's Anthropic Bias:
I found Chapters 1-5 on Bostrom's website at Will those chapters explain the error in my thinking? ETA: If someone could summarize the rebuttal contained in Bostrom's book, I would also appreciate it.
I tentatively agree with all the points you make above. This is a general principle: it shouldn't matter where or when the mind making a decision is, the decision should come out the same, given the same evidence. In the case of instrumental rationality, it results in the timeless decision theory (at least of my variety), where the mind by its own choice makes the same decision that its past instance would've precommited to make. In the case of prisoner's dilemma, the same applies to the conclusions made by the players running in parallel (as a special case). And in the cases of anthropic hazard, the same conclusions should be made by the target of the paradoxes and by the other agents. The genuine problems begin when the mind gets directly copied or otherwise modified in such a way that the representation of evidence gets corrupted, becoming incorrect for the target environment. Another source of genuine problems comes from indexical uncertainty, such as in the Sleeping Beauty problem, the case I didn't carefully think about yet. Which just might invalidate the whole of the above position about anthropics.
This is exactly what I was thinking. That someone won the lottery isn't improbable at all, and shouldn't be evidence of something weird going on, even for the person who won. Being the person who won the lottery three weeks in a row seems like something that shouldn't happen, but being right next to that guy seems like it would provide the same evidence.

Ha ha ha. Classic.

This is one of those stories you can show to would-be rationalists that will make them both laugh and think about probability. Well done.

If the hypothesis "this world is a holodeck" is normatively assigned a calibrated confidence well above 10-8, the lottery winner now has incommunicable good reason to believe they are in a holodeck. (I.e. to believe that the universe is such that most conscious observers observe ridiculously improbable positive events.)

Most conscious observers? I would think a universe/multiverse containing holodecks would still contain many people not in them. At best, you can conclude that most observers who don't see a world containing holodecks are in hol... (read more)

Just for fun: Not only are we living in someone's holodeck fantasy, it's a badly written holodeck fantasy!

(Taken from

Let me weigh in on what I consider to be the worst possible catastrophe of them all. One that would explain every stupidity in the world today. That we are living in a very poor simulation.


All right, the notion is gaining some degree of plausibility. But suppose it's true. In that case, whose simulation are we living in? Some vast future Omega Point consciousness?

... (read more)

That's the most amusing thing I've heard today. :)


After a lot of improbable things happen the main thing you have evidence for is that the universe is large enough to have improbable things happen. This could happen in MWI, or it could just happen in an ordinary very large universe. Or it could happen in a simulation that focuses on special events, so if your event is special this is also something that gets more support, relative to a small universe.

But I don't at all see how such events give you evidence about what sort of large universe you live in. And I don't see how winning the lottery is remotely unlikely enough to kick in such considerations.

I don't see how the size of the universe makes any difference - isn't it only the density of weird events that matters?
Unless the hypothesis under consideration is a particularly weird universe, the main way to get more weird events is to get more total events.
But if you get more weird events and more total events, the probability of a given event being weird remains constant. If it worked the way you said, you could also conclude a large universe based on normal events. This would violate conservation of expected evidence.

As I alluded to in a previous discussion this sort of thing is veering quickly into the territory of the small world phenomenon in human social networks.

With something likely to be remarked on in idle chatter with casual acquaintances, such as winning a lottery, you end up with a unexpectedly large likelihood of becoming aware of a small number of links from yourself to someone who had (Unusual Event X) occur to them.


For those unfamiliar with QTI, it's a simple simultaneous test of many-worlds plus a particular interpretation of anthropic observer-selection effects: You put a gun to your head and wire up the trigger to a quantum coinflipper. After flipping a million coins, if the gun still hasn't gone off, you can be pretty sure of the simultaneous truth of MWI+QTI.

Wouldn't any of several multiverse theories predict the survival outcome, and therefore you can't conclude that the quantum MWI is correct? That is, a world which is single, yet contains you infinitely ... (read more)

From a statistical standpoint, lottery winners don't exist - you would never encounter one in your lifetime, if it weren't for the selective reporting.

When you said that, it seemed to me that you were saying that you shouldn't play the lottery even if the expected payoff - or even the expected utility - were positive, because the payoff would happen so rarely.

Does that mean you have a formulation for rational behavior that maximizes something other than expected utility? Some nonlinear way of summing the utility from all possible worlds?

If someone sugg... (read more)

Broken intuition pump. The fact that money isn't utility (has diminishing returns) is actually very important here. I, for one, don't think I can envision pooling and redistributing actual utility, at least not well enough to draw any conclusions whatsoever. Also, a utility function might not be defined over selves at particular times, but over 4D universal histories, or even over the entire multiverse. (This is also relevant to your happiness vs. utility distinction, I think.)
What I'm getting at is that the decision society makes for how to distribute utility across different people, is very similar to the decision you make for how to distribute utility across your possible future selves. Why do we think it's reasonable to say that we should maximize average utility across all our possible future selves, when no one I know would say that we should maximize average utility across all living people?
Nothing so exotic. In game theory agents can be risk-averse, risk-neutral or risk-loving. This translates to convexity/concavity of the utility function.
0Paul Crowley
The winning payoff would have to be truly enormous for the expected utility to be positive.
-5Eliezer Yudkowsky

But what is your watching friend supposed to think? Though his predicament is perfectly predictable to you - that is, you expected before starting the experiment to see his confusion - from his perspective it is just a pure 100% unexplained miracle.

OK, I don't get this at all, but I totally understand the lottery example. I think Tyrrell McAllister raised this question, but only his other question was ever addressed. Are the two cases really the same? If so, how?

It's true that, as the person next to the gun, you should expect to live with the same prob... (read more)

Your friend does not predict higher odds of your survival conditional on many-worlds. Thus, your survival does not cause them to update upwards on many-worlds, and a high problility of many-worlds does not lessen the vast improbability of your survival. Hence a "miracle".

I get the feeling that I missed a lot of prediscussion to this topic. I am new here and new to these types of discussions, so if I am way off target please nudge me in the right direction. :)

If the statistics of winning a lottery are almost none, they are not none. As such, the chances of a lottery winner existing as time goes on increases with each lottery ticket purchased. (The assumption here is that "winner" simply means "holding the right ticket".)

Furthermore, it seems like the concept of the QTI is only useful if you already k... (read more)

I interpreted the last statement as follows: IF you assign a probability higher than 10^(-8) to the hypothesis that you are in a holodeck AND you win the lottery (which had a probabiltiy of 10^(-8) or thereabouts) THEN you have good reason to believe you're in a holodeck, because you've had such improbable good fortune. Correct me if I'm wrong on this.
3Paul Crowley
Strictly speaking you need to know the probability that you'll win the lottery given that you're on the holodeck to complete the calculation.
The person controlling the holodeck (who presumably designed the simulation) needs to know the probability. But the person being simulated, who experiences winning the lottery, does not need to know anything about the inner working of his (simulated) world. For the experience to seem real enough, it'd be best, even, not to know every detail of what's going on.
2Paul Crowley
I mean that if we're to know the evidential weight of winning the lottery to the theory that we're on the holodeck, we need to know P(L|H), so that we can calculate P(H|L) = P(L|H)P(H)/(P(L|H)P(H) + P(L|¬H)P(¬H)).
I get your point now. But all we need to know is whether P(L|H) > P(L|~H)*. If this is the case, then if an extremely unlikely (P(L/~H) -> 0) event L happens to you, this evidently increases the chance that you're in a holodeck simulation. In the formula, P(L|H) equates to (almost) 1 as P(L|~H) approaches zero. The unlikelier the event (amazons on unicorns descending from the heavens to take you to the land of bread and honey), i.e. the larger the difference between P(L|H) and P(L|~H), the larger the probability that you're experiencing a simulation. This is true as long as P(L|H) > P(L|~H). If L is a mundane event, P(L|H) = P(L|~H) and the formula reduces to P(H|L) = P(H). If L is so supremely banal that P(L|~H) > p(L|H), the occurence of L actually decreases the chance that you're experiencing a holodeck simulation. Indeed, I believe that was the point of the original post. The core assumption remains, of course, that you're more likely to win the lottery when you're experiencing a holodeck simulation than in the real world (P(L|H) > P(L|~H)). I'm not well-versed in Bayesian reasoning, so correct me if I'm wrong. Your posts have definitely helped to clarify my thoughts. *I don't know how to type the "not"-sign, so I'll use a tilde.

I've pondered a toned-down version of this argument in the context of religious experience and other hallucinations. Also, this is an important consideration for Utilitarian-style Pascalian religion.

I also knew someone whose family won the lottery, though I don't remember how much.

There are, of course, different degrees of lottery, and lottery winners. I take it that someone who wins (say) £20,000 is a lottery winner, but not really what Eliezer means.

I don't think it's an exception to the Agreement Theorem. All you have to do to to communicate the evidence is give your friend root access to your brain so he can verify you aren't lying. Of course Omega could have just rigged your brain so you think you survived a million QTI tests, but that possibility shouldn't worry your friend any more than it worries you.

also, BTW one of my Dad's ham radio buddies won the lottery recently.

How does this give him any more evidence? I don't believe lying was ever a hypothesis.