Regarding the first paragraph: every purported rational decision theory maps actions to expected values. In most decision theory thought experiments, the agent is assumed to know all the conditions of the scenario, and so they can be taken as absolute facts about the world leaving only the unknown random variables to feed into the decision-making process. In the Counterfactual Mugging, that is explicitly not true. The scenario states
you didn’t know about Omega’s little game until the coin was already tossed and the outcome of the toss was given to you
So it’s not enough to ask what a rational agent with full knowledge of the rest of the scenario should do. That’s irrelevant. We know it as omniscient outside observers, but the agent in question knows only what the mugger tells them. If they believe it then there is a reasonable argument that they should pay up, but there is nothing given in the scenario that makes it rational to believe the mugger. The prior evidence is massively against believing the mugger. Any decision theory that ignores this is broken.
Regarding the second paragraph: yes, indeed there is that additional argument against paying up and rationality does not preclude accepting that argument. Some people do in fact use exactly that argument even in this very much weaker case. It’s just a billion times stronger in the “Bob could have been Alice instead” case and makes rejecting the argument untenable.
Regarding the first paragraph: every purported rational decision theory maps actions to expected values. In most decision theory thought experiments, the agent is assumed to know all the conditions of the scenario, and so they can be taken as absolute facts about the world leaving only the unknown random variables to feed into the decision-making process. In the Counterfactual Mugging, that is explicitly not true. The scenario states
So it’s not enough to ask what a rational agent with full knowledge of the rest of the scenario should do. That’s irrelevant. We know it as omniscient outside observers, but the agent in question knows only what the mugger tells them. If they believe it then there is a reasonable argument that they should pay up, but there is nothing given in the scenario that makes it rational to believe the mugger. The prior evidence is massively against believing the mugger. Any decision theory that ignores this is broken.
Regarding the second paragraph: yes, indeed there is that additional argument against paying up and rationality does not preclude accepting that argument. Some people do in fact use exactly that argument even in this very much weaker case. It’s just a billion times stronger in the “Bob could have been Alice instead” case and makes rejecting the argument untenable.
Am I correct in assuming you don’t think one should give the money in the counterfactual mugging?