The way you set up the decision is not a fair test of belief, because the stakes are more like $1.50 to $99.
To fix that, we need to make 2 changes:
1) Let us give any reward/punishment to a third party we care about, e.g. SB.
2) The total reward/punishment she gets won’t depend on the number of people who make the decision. Instead, we will poll all of the survivors from all trials and pool the results (or we can pick 1 survivor at random, but let’s do it the first way).
The majority decides what guess to use, on the principle of one man, one vote. That is surely what we want from our theory—for the majority of observers to guess optimally.
Under these rules, if I know it’s the 1-shot case, I should guess red, since the chance is 50% and the payoff to SB is larger. Surely you see that SB would prefer us to guess red in this case.
OTOH if I know it’s the multi-shot case, the majority will be probably be blue, so I should guess blue.
In practice, of course, it will be the multi-shot case. The universe (and even the population of Earth) is large; besides, I believe in the MWI of QM.
The practical significance of the distinction has nothing to do with casino-style gambling. It is more that 1) it shows that the MWI can give different predictions from a single-world theory, and 2) it disproves the SIA.
Is that a “yes” or a “no” for the scenario as I posed it?
The way you set up the decision is not a fair test of belief.
I agree. It is only possible to fairly “test” beliefs when a related objective probability is agreed upon, which for us is clearly a problem. So my question remains unanswered, to see if we disagree behaviorally:
the stakes are more like $1.50 to $99.
That’s not my intention. To clarify, assume that:
the other prisoners’ decisions are totally independent of yours (perhaps they are irrational), so that you can in no sense effect 99 real other people to guess blue and achieve a $99 payoff with only one beating, and
the payoffs/beatings are really to the prisoners, not someone else,
Then, as I said, in that scenario I would guess that I’m in a blue room.
Would you really guess “red”, or do we agree?
(My “reasons” for blue would be to note that I started out overwhelmingly (99%) likely to be in a blue room, and that my surviving the subsequent coin toss is evidence that it did not land tails and kill blue-roomed prisoners, or equivalently, that counterfactual-typically, people guessing red would result in a great deal of torture. But please forget why; I just want to know what you would do.)
It is only possible to fairly “test” beliefs when a related objective probability is agreed upon
That’s wrong; behavioral tests (properly set up) can reveal what people really believe, bypassing talk of probabilities.
Would you really guess “red”, or do we agree?
Under the strict conditions above and the other conditions I have outlined (long-time-after, no other observers in the multiverse besides the prisoners), then sure, I’d be a fool not to guess red.
But I wouldn’t recommend it to others, because if there are more people, that would only happen in the blue case. This is a case in which the number of observers depends on the unknown, so maximizing expected average utility (which is appropriate for decision theory for a given observer) is not the same as maximizing expected total utility (appropriate for a class of observers).
More tellingly, once I find out the result (and obviously the result becomes known when I get paid or punished), if it is red, I would not be surprised. (Could be either, 50% chance.)
Not that I’ve answered your question, it’s time for you to answer mine: What would you vote, given that the majority of votes determines what SB gets? If you really believe you are probably in a blue room, it seems to me that you should vote blue; and it seems obvious that would be irrational.
Then if you find out it was red, would you be surprised?
So in my scenario, groups of people like you end up with 99 survivors being tortured or 1 not, with equal odds (despite that their actions are independent and non-competitive), and groups of people like me end up with 99 survivors not tortured or 1 survivor tortured, with equal odds.
Let’s say I’m not asserting that means I’m “right”. But consider that your behavior may be more due to a ritual of cognition rather than systematized winning.
You might respond that “rationalists win” is itself a ritual of cognition to be abandoned. More specifically, maybe you disagree that “whatever rationality is, it should fare well-in-total, on average, in non-competitive thought experiments”. I’m not sure what to do about that response.
No[w] that I’ve answered your question … What would you vote, given that the majority of votes determines what SB gets?
In your scenario, I’d vote red, because when the (independent!) players do that, her expected payoff is higher. More precisely, if I model the others randomly, me voting red increases the probability that SB lands in world with a majority “red” vote, increasing her expectation.
This may seem strange because I am playing by an Updateless strategy. Yes, in my scenario I act 99% sure that I’m in a blue room, and in yours I guess red, even though they have same assumptions regarding my location. Weird eh?
What’s happening here is that I’m planning ahead to do what wins, and planning isn’t always intuitively consistent with updating. Check out The Absent Minded Driver for another example where planning typically outperforms naive updating. Here’s another scenario, which involves interactive planning.
Then if you find out it was red, would you be surprised?
To be honest with you, I’m not sure how the “surprise” emotion is supposed to work in scenarios like this. It might even be useless. That’s why I base my actions on instrumental reasoning rather than rituals of cognition like “don’t act surprised”.
By the way, you are certainly not the first to feel the weirdness of time inconsistency in optimal decisions. That’s why there are so many posts working on decision theory here.
The way you set up the decision is not a fair test of belief, because the stakes are more like $1.50 to $99.
To fix that, we need to make 2 changes:
1) Let us give any reward/punishment to a third party we care about, e.g. SB.
2) The total reward/punishment she gets won’t depend on the number of people who make the decision. Instead, we will poll all of the survivors from all trials and pool the results (or we can pick 1 survivor at random, but let’s do it the first way).
The majority decides what guess to use, on the principle of one man, one vote. That is surely what we want from our theory—for the majority of observers to guess optimally.
Under these rules, if I know it’s the 1-shot case, I should guess red, since the chance is 50% and the payoff to SB is larger. Surely you see that SB would prefer us to guess red in this case.
OTOH if I know it’s the multi-shot case, the majority will be probably be blue, so I should guess blue.
In practice, of course, it will be the multi-shot case. The universe (and even the population of Earth) is large; besides, I believe in the MWI of QM.
The practical significance of the distinction has nothing to do with casino-style gambling. It is more that 1) it shows that the MWI can give different predictions from a single-world theory, and 2) it disproves the SIA.
Is that a “yes” or a “no” for the scenario as I posed it?
I agree. It is only possible to fairly “test” beliefs when a related objective probability is agreed upon, which for us is clearly a problem. So my question remains unanswered, to see if we disagree behaviorally:
That’s not my intention. To clarify, assume that:
the other prisoners’ decisions are totally independent of yours (perhaps they are irrational), so that you can in no sense effect 99 real other people to guess blue and achieve a $99 payoff with only one beating, and
the payoffs/beatings are really to the prisoners, not someone else,
Then, as I said, in that scenario I would guess that I’m in a blue room.
Would you really guess “red”, or do we agree?
(My “reasons” for blue would be to note that I started out overwhelmingly (99%) likely to be in a blue room, and that my surviving the subsequent coin toss is evidence that it did not land tails and kill blue-roomed prisoners, or equivalently, that counterfactual-typically, people guessing red would result in a great deal of torture. But please forget why; I just want to know what you would do.)
That’s wrong; behavioral tests (properly set up) can reveal what people really believe, bypassing talk of probabilities.
Under the strict conditions above and the other conditions I have outlined (long-time-after, no other observers in the multiverse besides the prisoners), then sure, I’d be a fool not to guess red.
But I wouldn’t recommend it to others, because if there are more people, that would only happen in the blue case. This is a case in which the number of observers depends on the unknown, so maximizing expected average utility (which is appropriate for decision theory for a given observer) is not the same as maximizing expected total utility (appropriate for a class of observers).
More tellingly, once I find out the result (and obviously the result becomes known when I get paid or punished), if it is red, I would not be surprised. (Could be either, 50% chance.)
Not that I’ve answered your question, it’s time for you to answer mine: What would you vote, given that the majority of votes determines what SB gets? If you really believe you are probably in a blue room, it seems to me that you should vote blue; and it seems obvious that would be irrational.
Then if you find out it was red, would you be surprised?
So in my scenario, groups of people like you end up with 99 survivors being tortured or 1 not, with equal odds (despite that their actions are independent and non-competitive), and groups of people like me end up with 99 survivors not tortured or 1 survivor tortured, with equal odds.
Let’s say I’m not asserting that means I’m “right”. But consider that your behavior may be more due to a ritual of cognition rather than systematized winning.
You might respond that “rationalists win” is itself a ritual of cognition to be abandoned. More specifically, maybe you disagree that “whatever rationality is, it should fare well-in-total, on average, in non-competitive thought experiments”. I’m not sure what to do about that response.
In your scenario, I’d vote red, because when the (independent!) players do that, her expected payoff is higher. More precisely, if I model the others randomly, me voting red increases the probability that SB lands in world with a majority “red” vote, increasing her expectation.
This may seem strange because I am playing by an Updateless strategy. Yes, in my scenario I act 99% sure that I’m in a blue room, and in yours I guess red, even though they have same assumptions regarding my location. Weird eh?
What’s happening here is that I’m planning ahead to do what wins, and planning isn’t always intuitively consistent with updating. Check out The Absent Minded Driver for another example where planning typically outperforms naive updating. Here’s another scenario, which involves interactive planning.
To be honest with you, I’m not sure how the “surprise” emotion is supposed to work in scenarios like this. It might even be useless. That’s why I base my actions on instrumental reasoning rather than rituals of cognition like “don’t act surprised”.
By the way, you are certainly not the first to feel the weirdness of time inconsistency in optimal decisions. That’s why there are so many posts working on decision theory here.