“However, before the experiment, you calculate the general utility of the conditional strategy “Reply ‘Yes’ to the question if you wake up in a green room” as (50% ((18 +$1) + (2 -$3))) + (50% ((18 -$3) + (2 +$1))) = -$20. You want your future selves to reply ‘No’ under these conditions.”
The sum given is the one you would perform if you did not know which room you woke up in. Surely a different sum is appropriate with the additional evidence that you awoke in a green room.
Incidentally, this problem seems far too complicated! I feel like the programmer faced with a bug report which failed to find some simple code that nontheless manages to reproduce the problem. Simplify, simplify, simplify!
The second sum still seems wrong. Here it is:
“However, before the experiment, you calculate the general utility of the conditional strategy “Reply ‘Yes’ to the question if you wake up in a green room” as (50% ((18 +$1) + (2 -$3))) + (50% ((18 -$3) + (2 +$1))) = -$20. You want your future selves to reply ‘No’ under these conditions.”
The sum given is the one you would perform if you did not know which room you woke up in. Surely a different sum is appropriate with the additional evidence that you awoke in a green room.
Incidentally, this problem seems far too complicated! I feel like the programmer faced with a bug report which failed to find some simple code that nontheless manages to reproduce the problem. Simplify, simplify, simplify!