At START, he is given the
option to be woken either at both intersections, or only at X. In the first
option he is absent-minded: when waking up, he does not know at which
intersection he is. We call the second option ‘‘clear-headedness.’’
As in the previous discussion, the question at X is not operative (what
to do) but only whether it makes sense to be ‘‘sorry.’’ If he chose
clear-headedness, his expectation upon reaching X is 1⁄4. If he had
chosen absent-mindedness, then when reaching X he would have attributed
probability 2⁄3 to being at X and 1⁄3 to being at Y.
I disagree. If I opt to be woken at X, then when I’m woken at intersection X, I know I’m at X. Even if the idea is that I’ll immediately go back to sleep, forget everything, and wake again at my payoff/destination, I still knew when I was woken at an intersection that it was X.
Unless I chose to be a) woken at X and b) have no memory of having chosen that, in which case it’s fair to say that “I’m at some intersection” (but they suppose I remember the road map I was given indicating intersectons/payoffs X,Y). I guess that’s what must have been meant.
If you remember your choice, then there’s no reason to ever choose ‘wake me up only at X’. If you wake up only at X, then you will either take action to turn off and score 0 points, or you will go back to sleep and continue to C and score 1 point.
0 or 1 is pretty bad, since you could then do better just by randomly picking from A, B, or C (as (1/3)*1 + (1/3)*4 + (1/3)*0 = 1.6...). Eliminating one branch entirely eliminates the problem.
From the paper:
I disagree. If I opt to be woken at X, then when I’m woken at intersection X, I know I’m at X. Even if the idea is that I’ll immediately go back to sleep, forget everything, and wake again at my payoff/destination, I still knew when I was woken at an intersection that it was X.
Unless I chose to be a) woken at X and b) have no memory of having chosen that, in which case it’s fair to say that “I’m at some intersection” (but they suppose I remember the road map I was given indicating intersectons/payoffs X,Y). I guess that’s what must have been meant.
I think it must’ve.
If you remember your choice, then there’s no reason to ever choose ‘wake me up only at X’. If you wake up only at X, then you will either take action to turn off and score 0 points, or you will go back to sleep and continue to C and score 1 point.
0 or 1 is pretty bad, since you could then do better just by randomly picking from A, B, or C (as (1/3)*1 + (1/3)*4 + (1/3)*0 = 1.6...). Eliminating one branch entirely eliminates the problem.