# The Sleeping Beauty paradox **URL:** \ **Category:** Great Debates\ **Created:** [April 12, 2009, 8:50pm UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882 "2009-04-12T20:50:53Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 12:07am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/101 "2009-04-16T00:07:32Z")
> [@Dr.Love](#): > > Like **begbert2** says, if you bet with your own gender you’ll be right 1000/1001 times. On the other hand, if you bet that men dominate, prior to examining your own gender, you’ll be right 50% of the time. Who says I’ll be right 1000/1001 times if I bet my own gender? Day 1: God flips the coin, it comes up heads. He creates me as the sole man on Earth. I bet my own gender dominates; I am wrong. God decides to destroy the universe and start over. Day 2: God flips the coin, it comes up heads. He creates me as one among 1000 men. I bet my own gender dominates; I am right. Destroy, restart. Day 3: Repeat of Day. Day 4: Repeat of Day 2. Etc. Half the days, the coin comes up heads, and half the days, it comes up tails, as would be expected from a fair coin. I bet my own gender dominates, but I’m right only 50% of the time, not 1000/1001 times, in this situation. OR Day 1: God flips the coin, it comes up heads. He creates me as the sole man on Earth. I bet my own gender dominates; I am wrong. Day 2: God flips the coin, it comes up tails. He creates me as the sole women on Earth. I bet my own gender dominates; I am wrong. Day 3: Repeat Day 1. Day 4: Repeat Day 2. Etc. Half the time, the coin comes up heads. But all the time, I’m wrong. OR Day 1: Coin comes up heads, I am created as sole man. Bet my own gender and am wrong. Day 2: Tails, I am sole woman. Bet own gender and am wrong. Day 3: Heads, but I’m not even created this time, just a bunch of other men and women. I don’t even get a chance to bet. Day 4: Tails, I am one among many women. Bet my own gender and am right. etc., in some complicated pattern, such that, in the end, even though the coin comes up heads half the time and tails half the time, I only get to bet 45% of the time, and out of those times, I’m only correct 13% of the time. What says it doesn’t work like any of these instead? In light of these, whence the conclusion “If you bet your own gender dominates, you’ll be right 1000/1001 times”? ---
**Author:** ![Dr.Love](https://avatars.discourse-cdn.com/v4/letter/d/e8c25b/32.png) [@Dr.Love](https://boards.straightdope.com/u/Dr.Love)\ **Post date:** [April 16, 2009, 12:11am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/102 "2009-04-16T00:11:46Z")
Situations like that are pretty standard in statistics. Everyone computes statistical tests to some level of confidence (maybe 90% or 95%), so even in the best scenario, one out of 20 statistical conclusions is wrong. Since everyone was guaranteed to meet someone of the opposing view, you can’t get any new information out of the situation, and so everyone should remain with their original conclusion. After all, they still have 1000/1001 chance of being correct. **Indistinguishable** , regarding your latest responce, I came up with something to address exactly that point, and decided against posting it. It’s the end of the workday here, so I’m going to head home. I think I should be able to get a responce up later this evening. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [April 16, 2009, 12:23am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/103 "2009-04-16T00:23:17Z")
> [@Indistinguishable](#): > > Well, now, supposing we take the exact same situation and add some communication: every night, at some point during during what would otherwise be your sleep, you are woken and paired with someone of the opposite gender to have a conversation. Afterwards, both your memories of the conversation are wiped (so no one can figure out “Hey, that’s a new face!”) and you’re sent back whence you came to get a good night’s rest. > > So one morning you wake up and see that you’re a man and you’re convinced “Wow, this means the coin almost certainly came up heads”. That night, you’re paired with a woman. You try to convince her of what you’ve been able to deduce, that the coin almost certainly came up heads (since you’ve observed yourself, in the morning, to be a man). But she, in turn, tries to convince you of what she’s been able to deduce, that the coin almost certainly came up tails (since she’s observed herself, in the morning, to be a woman). What’s going on here? Each of you thinks you have strong evidence for the coin flip going one way or another, but when you present it to the other, they wouldn’t find it convincing. Does that mean it wasn’t actually legitimately strong evidence in the first place? This is like if Monty Hall shows you a 1001 doors, one of which you randomly select to open, revealing a man. Then Monty Hall refers to his chart of room occupants and _deliberately selects_ another door, revealing a woman. The fact that Monty can find a woman is meaningless - he has the room occupant chart to refer to. Because he hasn’t given you any more meaningful information, you should not change your opinion. Amusingly, neither should the woman - from her perspective, she is a random one of the thousand, and you are a non-random selection matched to her. Of course, one of you is wrong - but we always knew that one man, or one woman, would be wrong. All that you know by meeting as described is that that one wrong person is in the room - which doesn’t hint at which one of you _is_ that person. Now, if you were allowed to open up another door at _random_ and then found a woman there, then you should waver - the random chances would balance out. And if you opened up _another_ door and found a woman, well, we’d be done 😃 -but if there were _two_ of one gender and a _two_ thousand of the other gender, finding the second random woman should make you nigh-certain that the rest are all women too. ---
**Author:** ![griffin1977](https://avatars.discourse-cdn.com/v4/letter/g/977dab/32.png) [@griffin1977](https://boards.straightdope.com/u/griffin1977)\ **Post date:** [April 16, 2009, 12:25am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/104 "2009-04-16T00:25:37Z")
My way of looking it would be this… The paradox is logically equivalent to doing this… Take a bowl and bunch of red/blue balls… Toss a coin If its heads put a single red ball into bowl If its tails put two blue balls into bowl What is the chance the coin toss was heads ? - 1/2 What is the chance a random ball is red ? - 1/3 No paradox there, its just two different questions. There is no “point of view” involved. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [April 16, 2009, 12:33am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/105 "2009-04-16T00:33:33Z")
> [@Indistinguishable](#): > > Who says I’ll be right 1000/1001 times if I bet my own gender? > > Day 1: God flips the coin, it comes up heads. He creates me as the sole man on Earth. I bet my own gender dominates; I am wrong. God decides to destroy the universe and start over. > Day 2: God flips the coin, it comes up heads. He creates me as one among 1000 men. I bet my own gender dominates; I am right. Destroy, restart. > Day 3: Repeat of Day. Day 4: Repeat of Day 2. Etc. Half the days, the coin comes up heads, and half the days, it comes up tails, as would be expected from a fair coin. > > I bet my own gender dominates, but I’m right only 50% of the time, not 1000/1001 times, in this situation. > > OR > > Day 1: God flips the coin, it comes up heads. He creates me as the sole man on Earth. I bet my own gender dominates; I am wrong. > Day 2: God flips the coin, it comes up tails. He creates me as the sole women on Earth. I bet my own gender dominates; I am wrong. > Day 3: Repeat Day 1. Day 4: Repeat Day 2. Etc. Half the time, the coin comes up heads. But all the time, I’m wrong. > > OR > > Day 1: Coin comes up heads, I am created as sole man. Bet my own gender and am wrong. > Day 2: Tails, I am sole woman. Bet own gender and am wrong. > Day 3: Heads, but I’m not even created this time, just a bunch of other men and women. I don’t even get a chance to bet. > Day 4: Tails, I am one among many women. Bet my own gender and am right. > etc., in some complicated pattern, such that, in the end, even though the coin comes up heads half the time and tails half the time, I only get to bet 45% of the time, and out of those times, I’m only correct 13% of the time. > > What says it doesn’t work like any of these instead? In light of these, whence the conclusion “If you bet your own gender dominates, you’ll be right 1000/1001 times”? Case three is invalid - only people who are created count. Imaginary uncreated people don’t - which is good, because there are an infinite amount of imaginary uncreated people. (If you’re trying to analogize not-created to not-being-asked, you’re mixing up the analogy; one of the _genders_ represents not-being-asked, give or take.) And in the first two cases, you’re ignoring that you’re not the only person on the planet. Everyone gets a vote, and if everyone bets their own gender, then they’re not (as an aggregate) wrong half the time, 1/1001th of the population is wrong, each and every time. The half part comes in the fact that half the time, that wrong person is a woman. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [April 16, 2009, 12:58am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/106 "2009-04-16T00:58:59Z")
> [@begbert2](#): > > (If you’re trying to analogize not-created to not-being-asked, you’re mixing up the analogy; one of the _genders_ represents not-being-asked, give or take.) Missed the edit window - this bit I said here is _completely_ wrong. :smack: The genders analogize the two different possible sequences of days; so in the original scenario only one gender/set of interrogations would _actually_ exist, when the dust settled. Of course, with probability we also consider the cases that don’t exist (though rarely do they get to meet and chat!), but that doesn’t excuse my cognitive flatulence here. If anything, the non-existent/non-conscious people analogize the days after the experiment is over, when no questions are being asked. Of course, in reality there are exactly as many total days one way or the other - so the question become not one of how many people/days there are, but rather what are the odds that you, being a random conscious person, are among the set with 1000 conscious people , as opposed to being in the set with 1 conscious person. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 2:02am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/107 "2009-04-16T02:02:45Z")
To the replies to my post #100: So even though the communicating man and the woman have the exact same information at their disposal (they know the exact same facts about the universe), they should come to different conclusions? ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 16, 2009, 2:05am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/108 "2009-04-16T02:05:23Z")
> [@Indistinguishable](#): > > To the replies to my last post: > So even though the man and the woman have the exact same information at their disposal (they know the exact same facts about the universe), they should come to different conclusions? Well, no, they know slightly different information. John knows that the creator would show him a woman if one existed, but he happened to be born a male; Joan knows that the creator would show him a man if one existed, but she happened to be born a female. Important distinction. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 2:07am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/109 "2009-04-16T02:07:08Z")
John also knows that the creator would show Joan a woman if one existed, but she happened to be born a female. Joan also knows that the creator would show John a man if one existed, but he happened to be born a male. They both know the same facts; after all, they’re in communication, so whatever one knows, the other finds out. Whatever empirical evidence the one has gathered, the other knows about as well. It’s as if they’ve both published papers on their findings and now have access to the same corpus of knowledge. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 2:19am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/110 "2009-04-16T02:19:27Z")
> [@Left\_Hand\_of\_Dorkness](#): > > John knows that the creator would show him a woman if one existed, but he happened to be born a male. Actually, although I quoted and re-used this line, looking back on it and trying to see what it means, it’s a weird thing to say, and I’m not sure what you were getting at with it; are you sure you understand the setup correctly? No matter what, at least one woman will exist, and no matter what, people are shown someone from the opposite gender. And John _is_ shown a woman. Precisely _because_ of (not in spite of) the fact that he was born a male. ---
**Author:** ![Alex\_Dubinsky](https://avatars.discourse-cdn.com/v4/letter/a/dbc845/32.png) [@Alex\_Dubinsky](https://boards.straightdope.com/u/Alex_Dubinsky)\ **Post date:** [April 16, 2009, 3:50am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/111 "2009-04-16T03:50:12Z")
> [@Indistinguishable](#): > > The right answer depends on whether you’re a man or a woman, why? That’s cool what you’re doing there. You’re trying to get freaked out by the idea that the act of observing changes what truth is. I’m not sure what to tell you. Maybe you’re not getting how trivial all this is. Maybe you’re onto something. Observation-changing-truth is basically the theme of quantum mechanics. And none of that stuff sounds anything as trivial as this. ---
**Author:** ![Alex\_Dubinsky](https://avatars.discourse-cdn.com/v4/letter/a/dbc845/32.png) [@Alex\_Dubinsky](https://boards.straightdope.com/u/Alex_Dubinsky)\ **Post date:** [April 16, 2009, 3:55am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/112 "2009-04-16T03:55:28Z")
> [@Indistinguishable](#): > > Well, now, supposing we take the exact same situation and add some communication: every night, at some point during during what would otherwise be your sleep, you are woken and paired with someone of the opposite gender to have a conversation. Afterwards, both your memories of the conversation are wiped (so no one can figure out “Hey, that’s a new face!”) and you’re sent back whence you came to get a good night’s rest. > > So one morning you wake up and see that you’re a man and you’re convinced “Wow, this means the coin almost certainly came up heads”. That night, you’re paired with a woman. You try to convince her of what you’ve been able to deduce, that the coin almost certainly came up heads (since you’ve observed yourself, in the morning, to be a man). But she, in turn, tries to convince you of what she’s been able to deduce, that the coin almost certainly came up tails (since she’s observed herself, in the morning, to be a woman). What’s going on here? Each of you thinks you have strong evidence for the coin flip going one way or another, but when you present it to the other, they wouldn’t find it convincing. Does that mean it wasn’t actually legitimately strong evidence in the first place? Hey! That’s just like special relativity! ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 4:11am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/113 "2009-04-16T04:11:22Z")
> [@Alex\_Dubinsky](#): > > Hey! That’s just like special relativity! In what respect? Special relativity implies that people with the same information should draw different conclusions? > [@Alex\_Dubinsky](#): > > That’s cool what you’re doing there. You’re trying to get freaked out by the idea that the act of observing changes what truth is. I’m not sure what to tell you. Maybe you’re not getting how trivial all this is. Maybe you’re onto something. Observation-changing-truth is basically the theme of quantum mechanics. And none of that stuff sounds anything as trivial as this. What does “observation-changing-truth” have to do with anything in my posts? (As as side note, I would not say “observation-changing-truth” is basically the theme of quantum mechanics, so much as the theme of pop culture bastardizations of quantum mechanics; I would think non-commuting operators and phased probability amplitudes (to be interpreted via the Born rule) are the theme of quantum mechanics. But I’m not really in a position to say…) ---
**Author:** ![Alex\_Dubinsky](https://avatars.discourse-cdn.com/v4/letter/a/dbc845/32.png) [@Alex\_Dubinsky](https://boards.straightdope.com/u/Alex_Dubinsky)\ **Post date:** [April 16, 2009, 4:23am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/114 "2009-04-16T04:23:24Z")
> [@Indistinguishable](#): > > In what respect? Special relativity implies that people with the same information should draw different conclusions? Well, this is rarely explained properly when dealing with time dilation, but that is the theme of the “twin paradox.” There is no such thing as “one twin went faster than the other and didn’t age.” Either twin can be said to be traveling faster than the other, and _each sees that it is the other who is aging slowly!_ I found it similar to how each gender is certain that it is the other that’s infrequent. > [@](#): > > (As as side note, I would not say “observation-changing-truth” is basically the theme of quantum mechanics, so much as the theme of pop culture bastardizations of quantum mechanics; I would think non-commuting operators and phased probability amplitudes (to be interpreted via the Born rule) are the theme of quantum mechanics. But I’m not really in a position to say…) Sure. Anyway, the act of observing is a pivotal thing in QM and underlies everything from the double-slit experiment to quantum computing. Incidentally, QM, like the SB riddle, is largely a study in probabilities. > [@](#): > > So even though the communicating man and the woman have the exact same information at their disposal (they know the exact same facts about the universe), they should come to different conclusions? Btw, I took this as the basis of my poetically-worded ‘observation-changing-truth’ comment, since I equate “reaching conclusions” to “figuring out the truth.” I mean.. they’re pretty much the same phrases as far as colloquial English is concerned, right? ---
**Author:** ![Dr.Love](https://avatars.discourse-cdn.com/v4/letter/d/e8c25b/32.png) [@Dr.Love](https://boards.straightdope.com/u/Dr.Love)\ **Post date:** [April 16, 2009, 4:37am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/115 "2009-04-16T04:37:11Z")
**Indistinguishable** : Like in all math, we have to make some assumptions in probability for the problems to be tractable. In the context of this problem, the natural assumption to make is the egalitarian one, that everyone is basically the same–that every potential person has an equal chance of filling any body. With this in mind, are your scenarios in post #101 meant to be random happenings, or examples of God screwing with you? If it’s the former, and we’re keeping our egalitarian assumption, then it’s possible to show mathematically that any infinite chain of events that does not have you waking up as a member of the majority 1000/1001 times has probability zero. If you mean the latter, then we’re outside of the scope of probability theory. If we’re going to drop the egalitarian assumption, then we need a reason to adopt another perspective. Back to post #100. If we’re keeping the egalitarian assumption, the man and the woman do not have the same information–they each know the gender of they body they drew in the random lottery. The fact that they meet at least one person of the other gender is deterministic, so it cannot affect our probabilistic beliefs. That people who draw different random outputs come to different conclusions is a basic fact of statistics. The fact that is covered up is that everyone believes they are right with certainty 1000/1001, and in fact 1000 out of 1001 people are right, so the probabilistic analysis is correct. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 5:15am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/116 "2009-04-16T05:15:44Z")
> [@Dr.Love](#): > > That people who draw different random outputs come to different conclusions is a basic fact of statistics. But, I assume, the situations you are referring to are ones where people draw different random outputs and then never see the others’. People who draw different random outputs but then afterwards share their data generally end up drawing the same conclusions, since they end up conditioning their priors on the same combined data… or do you have a basic statistical counterexample to this principle? Now, you could say, John and Joan don’t end up having the same combined data. John’s data is “I am male and you are female” while Joan’s data is “I am female and you are male.” But do we want to say that this kind of switch of deixis in phrasing a proposition (simply switching which referent gets called “I” and which gets called “you”) can substantively switch its implications? ---
**Author:** ![Dr.Love](https://avatars.discourse-cdn.com/v4/letter/d/e8c25b/32.png) [@Dr.Love](https://boards.straightdope.com/u/Dr.Love)\ **Post date:** [April 16, 2009, 5:36am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/117 "2009-04-16T05:36:44Z")
> [@Indistinguishable](#): > > But, I assume, the situations you are referring to are ones where people draw different random outputs and then never see the others’. People who draw different random outputs but then afterwards share their data generally end up drawing the same conclusions, since they end up conditioning their priors on the same combined data… or do you have a basic statistical counterexample to this principle? Under normal circumstances, yes, they should combine their data and reach a new conclusion. But in the hypothetical, the data that they get from sharing is entirely determined by the data they originally had. You meet someone of the opposite sex with probability 1 regardless of whether there are 1000 people of your sex or the opposite, so you can’t use the fact that you met someone of the opposite sex to support either conclusion. That’s why everyone comes out with the same probability estimate as they had going in. ---
**Author:** ![Isamu](https://avatars.discourse-cdn.com/v4/letter/i/7c8e57/32.png) [@Isamu](https://boards.straightdope.com/u/Isamu)\ **Post date:** [April 16, 2009, 5:38am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/118 "2009-04-16T05:38:57Z")
> [@Giles](#): > > Let’s look at it another way. I decide to go on vacation, and flip a coin to decide between: > (1) One night in London; > (2) Two nights in Paris. > (It’s more expensive in London). > > Next, I wake up in a strange hotel bed, and remember the decision-making process, but don’t remember which way the coin flip went. And (if it’s the second day) I can’t remember the first day – my short term memory is bad that way. > > So what are the odds between London and Paris? I think it’s obvious: 1/3 I’m in London, and 2/3 I’m in Paris. And I think the odds work the same for the question as originally posed: 1/3 heads, and 2/3 tails. I’m sure that if I remembered I’d based my destination decision on a coin toss, I’d still feel that there is equal likelihood of London or Paris (50/50). The same if I were sleeping beauty - 1/2. I can get the 1/3 answer, oversampling of one outcome, but I wouldn’t think like that IRL. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [April 16, 2009, 5:46am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/119 "2009-04-16T05:46:29Z")
> [@Dr.Love](#): > > Under normal circumstances, yes, they should combine their data and reach a new conclusion. But in the hypothetical, the data that they get from sharing is entirely determined by the data they originally had. You meet someone of the opposite sex with probability 1 regardless of whether there are 1000 people of your sex or the opposite, so you can’t use the fact that you met someone of the opposite sex to support either conclusion. That’s why everyone comes out with the same probability estimate as they had going in. Absolutely. Which, I am saying, perhaps suggests that they should both have the same probability estimate going in (I am reaching this potential conclusion by combining your specific observation that, in this case, each person’s prob going in = their prob going out with the plausible general principle that two people’s prob going out should be equal after they’ve shared data). ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [April 16, 2009, 6:12am UTC](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882/120 "2009-04-16T06:12:00Z")
> [@Indistinguishable](#): > > But, I assume, the situations you are referring to are ones where people draw different random outputs and then never see the others’. People who draw different random outputs but then afterwards share their data generally end up drawing the same conclusions, since they end up conditioning their priors on the same combined data… or do you have a basic statistical counterexample to this principle? > > Now, you could say, John and Joan don’t end up having the same combined data. John’s data is “I am male and you are female” while Joan’s data is “I am female and you are male.” But do we want to say that this kind of switch of deixis in phrasing a proposition (simply switching which referent gets called “I” and which gets called “you”) can substantively switch its implications? Actually, I’d say the difference in data they had was “I am one person, as likely to be one of the males in this group as anyone else in this group is, and I turned out to be male. You are a female and were specifically _chosen_ as female because I turned out to be male; whether there was one female or a thousand has no impact on the gender you turned out to be, because it was predetermined by the gender I happened to turn out to be.” The female has the reverse of that information; she knows that she is one individual out of a thousand and one, and she knows that the man she is presented with was selected from a smaller group that only included his gender. When they meet, neither _can_ see the other’s information, because they each know that that the other person was selected specifically for them, based on their gender, whereas they know that their own gender was _not_ selected from a similarly filtered set. Quite simply the perspective each has on their own existence assures that the information remains non-transferrable. Really this is very much like the usual Monty Hall question; there like here learning of the existence of something you already know (that there is at least _one_ person of the opposite gender/that at least _one_ of the other doors is wrong) tells you nothing and doesn’t change the odds of your original estimate being correct. (Of course, there the fact that one of the doors was removed from the set which collectively retains its 2:1 chance of being correct is helpful; here nothing is learned that changes anything.) [Previous page](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882.md?page=5) [Next page](https://boards.straightdope.com/t/the-sleeping-beauty-paradox/492882.md?page=7)