Omega's subcontracting to Alpha

by Stuart_Armstrong 1 min read16th Mar 201094 comments


This is a variant built on Gary Drescher's xor problem for timeless decision theory.

You get an envelope from your good friend Alpha, and are about to open it, when Omega appears in a puff of logic.

Being completely trustworthy as usual (don't you just hate that?), he explains that Alpha flipped a coin (or looked at the parity of a sufficiently high digit of pi), to decide whether to put £1000 000 in your envelope, or put nothing.

He, Omega, knows what Alpha decided, has also predicted your own actions, and you know these facts. He hands you a £10 note and says:

"(I predicted that you will refuse this £10) if and only if (there is £1000 000 in Alpha's envelope)."

What to do?

EDIT: to clarify, Alpha will send you the envelope anyway, and Omega may choose to appear or not appear as he and his logic deem fit. Nor is Omega stating a mathematical theorem: that one can deduce from the first premise the truth of the second. He is using XNOR, but using 'if and only if' seems a more understandable formulation. You get to keep the envelope whatever happens, in case that wasn't clear.