Omega can be replaced by amnesia

Bongo

Let's play a game. Two times, I will give you an amnesia drug and let you enter a room with two boxes inside. Because of the drug, you won't know whether this is the first time you've entered the room. On the first time, both boxes will be empty. On the second time, box A contains $1000, and Box B contains $1,000,000 iff this is the second time and you took only box B the first time. You're in the room, do take both boxes or only box B?

This is equivalent to Newcomb's Problem in the sense that any strategy does equally well on both, where by "strategy" I mean a mapping from info to (probability distributions over) actions.

I suspect that any problem with Omega can be transformed into an equivalent problem with amnesia instead of Omega.

Does CDT return the winning answer in such transformed problems?

Discuss.

Let's play a game. Two times, I will give you an amnesia drug and let you enter a room with two boxes inside. Because of the drug, you won't know whether this is the first time you've entered the room. On the first time, both boxes will be empty. On the second time, box A contains $1000, and Box B contains $1,000,000 iff this is the second time and you took only box B the first time. You're in the room, do take both boxes or only box B?

This is equivalent to Newcomb's Problem in the sense that any strategy does equally well on both, where by "strategy" I mean a mapping from info to (probability distributions over) actions.

I suspect that any problem with Omega can be transformed into an equivalent problem with amnesia instead of Omega.

Does CDT return the winning answer in such transformed problems?

Discuss.

offer the player two boxes, the first one contains $1K, the second contains $1M, taking both boxes triggers a bomb that destroys the second box.

Hmm. This form has the same expected winnings for all strategies, but the $0 and $1,001,000 outcomes are impossible, unlike in the transformed Newcomb and the original Newcomb (given an Omega that doesn't punish mixed strategies). Also, expected winnings doesn't equal expected utility. For some utility functions, your problem has different expected utility than the normal or amnesiac Newcomb even if you play the same strategy in each. So it's not really equivalent.

Another example: consider (the tranformation of) Parfit's Hitchiker. If you use a coinflipping strategy there, the expected utility is

0.5*U(die)+0.5*(0.5*U($0)+0.5*U(-$100) = 0.5*U(die)+0.25*U($0)+0.25*U(-$100)

While the expected utility in the version where you simply plop the player in front of an ATM and drive them to the desert and dump them there if they don't pay $100 is:

0.5*U(die) + 0.5-U(-$100)

Which is clearly different.

Your transformation seems to require weird Omegas that respond to randomizing players by randomizing too. It's not clear to me why an Omega would want to behave like that (probabilistically reward cheaters). Can you handle other kinds of Omegas, e.g. the original kind specified by Eliezer?

23

Omega can be replaced by amnesia

23

23

23

Omega can be replaced by amnesia

23

23