I’ve always been a one-boxer. I think I have a new solution as to why. Try this:
Scenario A: you will take a sleep potion and be woken up twice during the middle of the night to be asked to take one box or both boxes. Whatever you do the first time determines whether $1m is placed in the potentially-empty box. Whatever you do the second time determines what you collect. The catch is that the sleep potion will wipe all your memories over the next twelve hours. You’re told this in advance and asked to make up your mind. So you’ll give the same answer each time [or if you employ a mixed strategy, employ the same mixed strategy, because you don’t know if you’ve already been woken up].
If you say “one box” each time, you collect $1,000,000
If you say “both boxes” each time, you collect $1,000.
So you know, given this, that you do better to say “one box”. Do two-boxers agree with this?
Scenario B: Same as scenario A, except that instead of being woken up twice during the night, you will be woken up once and asked which boxes you will take. Your thoughts now are read by an expert mind-reading device. Whatever you plan to say will be used to determine whether there is $1m or $0 in the box you surely take. I think that you still take one box. Do two-boxers agree with this?
Scenario C: Same as scenario B, except that instead of having your thoughts read now, your thoughts are predicted by an expert thought-predicting device. This is then used to determine what will be placed in the box of uncertain contents. I hold that having your thoughts known at the time and known before you will think them are identical for the purposes of this problem. [mind-blowing in many respects, I agree, but irrelevant for this problem.] Ergo I take one box. Do two-boxers agree?
As a 1.4999999999999 boxer (i.e. take a quantum randomness source for [0, 1], take both boxes if 0, one box if 1, one box if something else happens), I don’t think scenario C is convincing.
The crucial property of B is that as your thoughts change the contents of the box change. The casualty link goes forward in time. Thus the right decision is to take one box, as by the act of taking one box, you will make it contain the money.
In C however there is no such casualty. The oracle either put money in both boxes, or it did not. Your decision now cannot possibly affect that state. So you cannot base your decision in C on its similarity to B.
A good reason to one box, in my opinion, is that before you encounter the boxes it is clearly preferable to commit to one boxing. This is of course not compatible with taking two boxes when you find them (because the oracle seems to be perfect). So it is rational to make yourself the kind of person that takes one box (because you know this brings you the best benefit, short of using the randomness trick).
I’ve always been a one-boxer. I think I have a new solution as to why. Try this: Scenario A: you will take a sleep potion and be woken up twice during the middle of the night to be asked to take one box or both boxes. Whatever you do the first time determines whether $1m is placed in the potentially-empty box. Whatever you do the second time determines what you collect. The catch is that the sleep potion will wipe all your memories over the next twelve hours. You’re told this in advance and asked to make up your mind. So you’ll give the same answer each time [or if you employ a mixed strategy, employ the same mixed strategy, because you don’t know if you’ve already been woken up].
If you say “one box” each time, you collect $1,000,000 If you say “both boxes” each time, you collect $1,000.
So you know, given this, that you do better to say “one box”. Do two-boxers agree with this?
Scenario B: Same as scenario A, except that instead of being woken up twice during the night, you will be woken up once and asked which boxes you will take. Your thoughts now are read by an expert mind-reading device. Whatever you plan to say will be used to determine whether there is $1m or $0 in the box you surely take. I think that you still take one box. Do two-boxers agree with this?
Scenario C: Same as scenario B, except that instead of having your thoughts read now, your thoughts are predicted by an expert thought-predicting device. This is then used to determine what will be placed in the box of uncertain contents. I hold that having your thoughts known at the time and known before you will think them are identical for the purposes of this problem. [mind-blowing in many respects, I agree, but irrelevant for this problem.] Ergo I take one box. Do two-boxers agree?
As a 1.4999999999999 boxer (i.e. take a quantum randomness source for [0, 1], take both boxes if 0, one box if 1, one box if something else happens), I don’t think scenario C is convincing.
The crucial property of B is that as your thoughts change the contents of the box change. The casualty link goes forward in time. Thus the right decision is to take one box, as by the act of taking one box, you will make it contain the money.
In C however there is no such casualty. The oracle either put money in both boxes, or it did not. Your decision now cannot possibly affect that state. So you cannot base your decision in C on its similarity to B.
A good reason to one box, in my opinion, is that before you encounter the boxes it is clearly preferable to commit to one boxing. This is of course not compatible with taking two boxes when you find them (because the oracle seems to be perfect). So it is rational to make yourself the kind of person that takes one box (because you know this brings you the best benefit, short of using the randomness trick).