I do want to add—separately—that superrational agents (not sure about EDT) can solve this problem in a roundabout way.
Imagine if some prankster erased the “1” and “2″ from the signs in rooms A1 and A2, leaving just “A” in both cases. Now everyone has less information and makes better decisions. And in the real contest, (super)rational agents could achieve the same effect by keeping their eyes closed. Simply say “tails,” maximize expected value, and leave the room never knowing which one it was.
None of which should be necessary. (Super)rational agents should win even after looking at the sign. They should be able to eliminate a possibility and still guess “tails.” A flaw must exist somewhere in the argument for “heads,” and even if I haven’t found that flaw, a perfect logician would spot it no problem.
I do want to add—separately—that superrational agents (not sure about EDT) can solve this problem in a roundabout way.
Imagine if some prankster erased the “1” and “2″ from the signs in rooms A1 and A2, leaving just “A” in both cases. Now everyone has less information and makes better decisions. And in the real contest, (super)rational agents could achieve the same effect by keeping their eyes closed. Simply say “tails,” maximize expected value, and leave the room never knowing which one it was.
None of which should be necessary. (Super)rational agents should win even after looking at the sign. They should be able to eliminate a possibility and still guess “tails.” A flaw must exist somewhere in the argument for “heads,” and even if I haven’t found that flaw, a perfect logician would spot it no problem.