Undoubtedly this has come up before, but I want to pose this puzzle in a particular way.
You have two closed boxes and there is money in one of them. You have a choice of opening one box or both boxes and you get to keep any money you find. You are informed that the machine which loaded the money was able to predict your choice and has put $1,000,000 in box A if it predicted you chose just box A and $1,000 in box B if it predicted you chose both boxes.
You check and find that this machine has always made perfect predictions in the past, including in situations just like this. You have done your homework sufficiently to be sure there has been no trickery.
The question is, do you open just one box, or do you open both?
One answer says that your choice cannot change what is in the boxes and so you will get as much money as it is possible to get by opening both.
Now I say that there is a flaw in that. It assumes that you have a choice in the matter - that it is possible for you to open just one box, or to open both boxes.
But, by the premises of the puzzle, something has consistently made perfect predictions of people's choices and so it is highly likely that you have no choice in the matter, the fact of which you will do is already inevitable, you just don't know which yet.
If you have no choice in the matter and the machine makes perfect prediction then the amount of money in the box is correlated to your choice.
So your reasoning should be "The choice I make is already inevitable and the box loading machine has predicted this and loaded the boxes accordingly. If it turns out that I choose both boxes then I will only get $1,000. If it turns out that I choose just box A then I will get $1,000,000. So I should try to choose box A (if this is possible) and I will be guaranteed $1,000,000".
If you are not convinced yet and think "both boxes" is still the right answer then suppose you had given this advice one year ago. By the premises of the puzzle the machine is always observed to get it right and there has never been a single instance where it has got it wrong, including cases just like this. And so for the past year the people who took your advice only got $1,000 and the people who ignored your advice and chose just box A always got $1,000,000. Some people come to you and ask that if there is anything about this that would make you change your advice, and if not why do you expect something to change and advice which has proved disastrously wrong for the past year will start being sound.
What would you say?
You have two closed boxes and there is money in one of them. You have a choice of opening one box or both boxes and you get to keep any money you find. You are informed that the machine which loaded the money was able to predict your choice and has put $1,000,000 in box A if it predicted you chose just box A and $1,000 in box B if it predicted you chose both boxes.
You check and find that this machine has always made perfect predictions in the past, including in situations just like this. You have done your homework sufficiently to be sure there has been no trickery.
The question is, do you open just one box, or do you open both?
One answer says that your choice cannot change what is in the boxes and so you will get as much money as it is possible to get by opening both.
Now I say that there is a flaw in that. It assumes that you have a choice in the matter - that it is possible for you to open just one box, or to open both boxes.
But, by the premises of the puzzle, something has consistently made perfect predictions of people's choices and so it is highly likely that you have no choice in the matter, the fact of which you will do is already inevitable, you just don't know which yet.
If you have no choice in the matter and the machine makes perfect prediction then the amount of money in the box is correlated to your choice.
So your reasoning should be "The choice I make is already inevitable and the box loading machine has predicted this and loaded the boxes accordingly. If it turns out that I choose both boxes then I will only get $1,000. If it turns out that I choose just box A then I will get $1,000,000. So I should try to choose box A (if this is possible) and I will be guaranteed $1,000,000".
If you are not convinced yet and think "both boxes" is still the right answer then suppose you had given this advice one year ago. By the premises of the puzzle the machine is always observed to get it right and there has never been a single instance where it has got it wrong, including cases just like this. And so for the past year the people who took your advice only got $1,000 and the people who ignored your advice and chose just box A always got $1,000,000. Some people come to you and ask that if there is anything about this that would make you change your advice, and if not why do you expect something to change and advice which has proved disastrously wrong for the past year will start being sound.
What would you say?
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