She doesn’t have a probability on a particular room or of a coin result as of Monday because she doesn’t observe that on Monday.
Pertinent comment, so I’ve added an of observing the coin.
I’ve got a different scenario with no duplicates. A fair coin is flipped today, if it’s heads, Roulette Rory gets killed with 75% probability before learning what the coin says.
In this case, not making an observation (due to death) is another possible history. The possible future histories are “see heads”, “see tails”, and “{}” (see the other post on how deaths don’t affect Bayesian probability).
That’s also the reason why ID(Sleeping Beauty) doesn’t have the paradox; the duplicates existing but not observing their history means that heads Sleeping Beauty gains information on Monday (I’m not dead, hence I wasn’t the duplicate that died).
I don’t think the epsilon chance of observing now really helps. It makes the current probabilities meaningful but you still have no particular reason to insist that the current probabilities (“what happens if I were to observe this today”) matches the future probabilities (“what happens if I observe it in the future”), given that the observations are correlated.
Re death, it just doesn’t seem different to me. If I can magically increase my probability in outcome A by committing to suicide in not-A worlds, I can also increase my probability in A by duplicating myself in A worlds. You’ve set up a formalism that allows the former and not the latter, then you’re pointing to a contradiction. But they’re both about as mysterious and settled the same way. The first isn’t controversial and the second shouldn’t be either.
(The exact probabilities still depend on SSA vs SIA vs others. But the fact that they won’t match the objective probabilities seems fine.)
If I can magically increase my probability in outcome A by committing to suicide in not-A worlds
You can’t. You can increase your relative probability of seeing outcome A, conditional on you being alive. You split into: see A, see not A, be dead. Both of the later are in world not A, and you can shift their relative size, but not their total size.
It’s survivorship bias via suicide, nothing strange about it.
Any conditional duplication is (for the purposes of the scenario’s credence of heads when asked) identical to unconditionally duplicating and then killing the duplicate in room 2 on heads before awakening.
What’s more, it’s the same as just not asking the duplicate in room 2 on heads, without any killing involved.
What’s more, it doesn’t matter when that duplication happens prior to being asked, before the coin flip or after, so longer as neither knows which one is going to be asked on heads.
I’m not sure whether you’re agreeing with my first point or not, regarding the equivalence of conditional duplication with unconditional duplication + conditional killing.
Since you said that the martingale condition is fully satisfied for both unconditional duplication and for conditional killing, do you believe that it is necessarily (regardless of SIA belief) satisfied for the sequence of both?
It’s the equivalence between (conditional duplication) and (unconditional duplication + conditional killing) that I’m disputing (or at least saying that you can’t just assume for free).
The difference is clear for the formal martingale: let’s count the full agent histories from beginning to end. Conditional duplication has three histories - (Sunday, awake, room 1, T), (Sunday, awake, room 2, T) and (Sunday, awake, room 1, H). While (unconditional duplication + conditional killing) has four—those three plus extra one heads: the “death” history of just (Sunday).
Thus the martingale in the (ud + ck) case has an extra possible future observation to consider: specifically, the non-observation. That’s why “awake” gives information in the (ud+ck) case (not all your duplicates would be guaranteed to see it) but not in the (cd) case (where all your duplicates are guaranteed to see it).
(It doesn’t help if one says that “non-observations don’t count”, because then the theory breaks breaks the martingale in the case of just “conditional killing” on its own.)
Now, philosophically, I’m partial to the idea that “instant duplication followed by deletion” should be the same as “not creating duplicates at all”; that’s a strong pro-SIA argument. But that doesn’t fix the martingale; it instead shows that if we assumed that there were instantly-deleted duplicates, then that assumption would fix the martingale.
I consider the cd = ud+ck equivalence to be much more fundamental than any martingale property, so I guess that’s the difference.
If we have an epistemic model in which we need to consider whether or not a duplicate was created and destroyed without ever making any observations, then as I see it that model should be discarded as it contains internal flaws. It shouldn’t even make any difference if we bring in an inert lump of random matter instead of a non-conscious duplicate, either. From an epistemic point of view, all non-observers are equivalently irrelevant.
Sure, but then why is it strange to do the same with duplication? You’re shifting your relative probability of seeing A, by creating extra versions of you that see A.
Predicted observation. You know you’ll be observing waking up on Monday (or, at least, that every thread going on from you to will observe waking up on Monday). And yet you are not, now, currently in the epistemic state you will be on Monday, despite know exactly what you will observe.
Bbtw, death and birth/creating are opposites, and neither is really a problem in anthropic probability. The opposite of duplication is merger—much more difficult to achieve, but, yes, it has similar issues to duplication.
“The thread of my experience has forked/merged” is something probability theories were not built to deal with; unlike threads of experience ending and starting, which is can deal with fine.
Every thread going on from you will observe something in Roulette too. (The threads that die don’t go on from you, then.)
When predicting your future experiences, you automatically condition on the fact that there will be future experiences, so they won’t always match objective probabilities. And you can also adjust for some versions of you having more experiences than others.
It’s more fragile than that. E.g. suppose a coin is flipped and on tails, you’ll be given a false memory of being asked your credence for heads, and answering “100%”. On heads you’ll simply be asked the question with no memory alterations. Then in both cases you’ll be asked “are you sure?”
If you’re in the situation of remembering having been asked the question but not answering, then you must be in the heads case, and should answer “100%”. But then when you’re asked “are you sure”, you are no longer sure because you now have exactly the same sort of memories that would have had in the tails case. Your memory hasn’t been altered in this case and you have no new information, so why are you now uncertain about something you were previously rationally certain of?
Sorry, the latex display should be fixed now.
Pertinent comment, so I’ve added an
In this case, not making an observation (due to death) is another possible history. The possible future histories are “see heads”, “see tails”, and “{}” (see the other post on how deaths don’t affect Bayesian probability).
That’s also the reason why ID(Sleeping Beauty) doesn’t have the paradox; the duplicates existing but not observing their history means that heads Sleeping Beauty gains information on Monday (I’m not dead, hence I wasn’t the duplicate that died).
I don’t think the epsilon chance of observing now really helps. It makes the current probabilities meaningful but you still have no particular reason to insist that the current probabilities (“what happens if I were to observe this today”) matches the future probabilities (“what happens if I observe it in the future”), given that the observations are correlated.
Re death, it just doesn’t seem different to me. If I can magically increase my probability in outcome A by committing to suicide in not-A worlds, I can also increase my probability in A by duplicating myself in A worlds. You’ve set up a formalism that allows the former and not the latter, then you’re pointing to a contradiction. But they’re both about as mysterious and settled the same way. The first isn’t controversial and the second shouldn’t be either.
(The exact probabilities still depend on SSA vs SIA vs others. But the fact that they won’t match the objective probabilities seems fine.)
You can’t. You can increase your relative probability of seeing outcome A, conditional on you being alive. You split into: see A, see not A, be dead. Both of the later are in world not A, and you can shift their relative size, but not their total size.
It’s survivorship bias via suicide, nothing strange about it.
Any conditional duplication is (for the purposes of the scenario’s credence of heads when asked) identical to unconditionally duplicating and then killing the duplicate in room 2 on heads before awakening.
What’s more, it’s the same as just not asking the duplicate in room 2 on heads, without any killing involved.
What’s more, it doesn’t matter when that duplication happens prior to being asked, before the coin flip or after, so longer as neither knows which one is going to be asked on heads.
So the duplication isn’t the problem.
SIA (which I tend to agree with) treats unconditional and conditional duplication as the same; but that’s an assumption we don’t get to take for free.
On heads, being killed or not being asked have clear effects in terms of expectation of alternative observations to see or not see.
That’s why unconditional duplication is fully martingale, while conditional duplication isn’t.
I’m not sure whether you’re agreeing with my first point or not, regarding the equivalence of conditional duplication with unconditional duplication + conditional killing.
Since you said that the martingale condition is fully satisfied for both unconditional duplication and for conditional killing, do you believe that it is necessarily (regardless of SIA belief) satisfied for the sequence of both?
If not, how does the first equivalence break?
Yep, the martingale is satisfied for both.
It’s the equivalence between (conditional duplication) and (unconditional duplication + conditional killing) that I’m disputing (or at least saying that you can’t just assume for free).
The difference is clear for the formal martingale: let’s count the full agent histories from beginning to end. Conditional duplication has three histories - (Sunday, awake, room 1, T), (Sunday, awake, room 2, T) and (Sunday, awake, room 1, H). While (unconditional duplication + conditional killing) has four—those three plus extra one heads: the “death” history of just (Sunday).
Thus the martingale in the (ud + ck) case has an extra possible future observation to consider: specifically, the non-observation. That’s why “awake” gives information in the (ud+ck) case (not all your duplicates would be guaranteed to see it) but not in the (cd) case (where all your duplicates are guaranteed to see it).
(It doesn’t help if one says that “non-observations don’t count”, because then the theory breaks breaks the martingale in the case of just “conditional killing” on its own.)
Now, philosophically, I’m partial to the idea that “instant duplication followed by deletion” should be the same as “not creating duplicates at all”; that’s a strong pro-SIA argument. But that doesn’t fix the martingale; it instead shows that if we assumed that there were instantly-deleted duplicates, then that assumption would fix the martingale.
I consider the cd = ud+ck equivalence to be much more fundamental than any martingale property, so I guess that’s the difference.
If we have an epistemic model in which we need to consider whether or not a duplicate was created and destroyed without ever making any observations, then as I see it that model should be discarded as it contains internal flaws. It shouldn’t even make any difference if we bring in an inert lump of random matter instead of a non-conscious duplicate, either. From an epistemic point of view, all non-observers are equivalently irrelevant.
I agree about 75% with this perspective.
Sure, but then why is it strange to do the same with duplication? You’re shifting your relative probability of seeing A, by creating extra versions of you that see A.
Predicted observation. You know you’ll be observing waking up on Monday (or, at least, that every thread going on from you to will observe waking up on Monday). And yet you are not, now, currently in the epistemic state you will be on Monday, despite know exactly what you will observe.
Bbtw, death and birth/creating are opposites, and neither is really a problem in anthropic probability. The opposite of duplication is merger—much more difficult to achieve, but, yes, it has similar issues to duplication.
“The thread of my experience has forked/merged” is something probability theories were not built to deal with; unlike threads of experience ending and starting, which is can deal with fine.
I don’t buy this distinction.
Every thread going on from you will observe something in Roulette too. (The threads that die don’t go on from you, then.)
When predicting your future experiences, you automatically condition on the fact that there will be future experiences, so they won’t always match objective probabilities. And you can also adjust for some versions of you having more experiences than others.
It’s more fragile than that. E.g. suppose a coin is flipped and on tails, you’ll be given a false memory of being asked your credence for heads, and answering “100%”. On heads you’ll simply be asked the question with no memory alterations. Then in both cases you’ll be asked “are you sure?”
If you’re in the situation of remembering having been asked the question but not answering, then you must be in the heads case, and should answer “100%”. But then when you’re asked “are you sure”, you are no longer sure because you now have exactly the same sort of memories that would have had in the tails case. Your memory hasn’t been altered in this case and you have no new information, so why are you now uncertain about something you were previously rationally certain of?