Extremely Counterfactual Mugging or: the gist of Transparent Newcomb

Bongo

Omega will either award you $1000 or ask you to pay him $100. He will award you $1000 if he predicts you would pay him if he asked. He will ask you to pay him $100 if he predicts you wouldn't pay him if he asked.

Omega asks you to pay him $100. Do you pay?

This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.

Here's a diagram:

Omega will either award you $1000 or ask you to pay him $100. He will award you $1000 if he predicts you would pay him if he asked. He will ask you to pay him $100 if he predicts you wouldn't pay him if he asked.

Omega asks you to pay him $100. Do you pay?

This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.

Here's a diagram:

To predict, Omega doesn't need to simulate. You can predict that water will boil when put on fire without simulating the movement of 10^23 molecules.

Omega even can't use simulation to arrive at his prediction in this scenario. If Omega demands money from simulated agents who then agree to pay, the simulation violates the formulation of the problem, according to which Omega should reward those agents.

If the problem is reformulated as "Omega demands payment only if the agent would counterfactually disagree to pay, OR in a simulation", then we have a completely different problem. For example, if the agent is sufficiently confident about his own decision algorithm, then after Omega's demand he could assign high probability to being in a simulation. The analysis would be more complicated there.

In short, I am only saying that

Omega is trustworthy.
Omega can predict the agents behaviour with certainty.
Omega tells that it demands money only from agents whom it predicted to reject the demand.
Omega demands the money.
The agent pays.

are together incompatible statements.

You can predict that water will boil when put on fire without simulating the movement of 10^23 molecules.

True but irrelevant. In order to make an accurate prediction, Omega needs, at the very least, to simulate my decision-making faculty in all significant aspects. If my decision-making process decides to recall some particular memory, then Omega needs to simulate that memory in all significant aspects. If my decision-making process decides to wander around the room conducting physics experiments, just to be a jackass, and to peg my decision to the r... (read more)