I have a similar confusion. I thought the definition of winning is objective (and frequentist): after a large number of identically set up experiments, the winning decision is the one that gains the most value. In Newcomb’s it’s one-boxing, in twin prisoner dilemma it’s cooperating, in other PDs it depends on the details of your opponent and on your knowledge of them, in counterfactual mugging it depends on the details of how trustworthy the mugger is, on whom it chooses to pay or charge, etc, the problem is underspecified as presented. If you have an “unfair” Omega who punishes a specific DT agent, the winning strategy is to be the Omega-favored agent.
There is no need for counterfactuals, by the way, just calculate what strategy nets the highest EV. Just like with Newcomb’s, in some counterfactual mugger setups only the agents who pay when lost get a chance to win. If you are the type of agent who doesn’t pay, the CFM predictor will not give you a chance to win. This is like a lottery, only you pay after losing, which does not matter if the predictor knows what you would do. Not paying when losing is equivalent to not buying a lottery ticket when the expected winning is more than the ticket price. I don’t know if this counts as decision theory, probably not.
I have a similar confusion. I thought the definition of winning is objective (and frequentist): after a large number of identically set up experiments, the winning decision is the one that gains the most value. In Newcomb’s it’s one-boxing, in twin prisoner dilemma it’s cooperating, in other PDs it depends on the details of your opponent and on your knowledge of them, in counterfactual mugging it depends on the details of how trustworthy the mugger is, on whom it chooses to pay or charge, etc, the problem is underspecified as presented. If you have an “unfair” Omega who punishes a specific DT agent, the winning strategy is to be the Omega-favored agent.
There is no need for counterfactuals, by the way, just calculate what strategy nets the highest EV. Just like with Newcomb’s, in some counterfactual mugger setups only the agents who pay when lost get a chance to win. If you are the type of agent who doesn’t pay, the CFM predictor will not give you a chance to win. This is like a lottery, only you pay after losing, which does not matter if the predictor knows what you would do. Not paying when losing is equivalent to not buying a lottery ticket when the expected winning is more than the ticket price. I don’t know if this counts as decision theory, probably not.