And this is the problem I have with all the Newcomb/Omega business.
The hypothetical should be fought. We should no more assign absolute certainty to Omega’s predictive power than we should assign absolute certainty to CDT’s predictive power.
Instead of assigning 0 probability to the theory that Omega can make a mistake, assign DeltaOmega. Similarly assign DeltaCDT to the probability that CDT analysis is wrong. I’m too lazy to actually do the math, but do you have any doubt that the right decision will depend on the ratio of the two deltas?
There’s really nothing to see here. .This is just another case of generating paradoxes in probability theory when you don’t do a full analysis using finite, non zero probability assignments.
This is a similar issue the OP has come up against. Proposition1 is that A obeys certain game theoretic rules. Proposition2 is the report that implicates A violating those rules. When your propositions seem mutually contradictory, because you have lazily assigned 0 probability to them, hilarity ensues. Assign finite values, and the mysteries are resolved.
You are basically using the trembling hand equilibrium concept. I picked the payoffs so this would not yield an easy solution. Consider an equilibrium where Player 1 intends to pick A, but there is a small but equal chance he will pick B or C by mistake. In this equilibrium Player 2 would pick Y if he got to move, but then Player 1 would always intend to Pick C, effectively pretending he had made a mistake.
And this is the problem I have with all the Newcomb/Omega business.
The hypothetical should be fought. We should no more assign absolute certainty to Omega’s predictive power than we should assign absolute certainty to CDT’s predictive power.
Instead of assigning 0 probability to the theory that Omega can make a mistake, assign DeltaOmega. Similarly assign DeltaCDT to the probability that CDT analysis is wrong. I’m too lazy to actually do the math, but do you have any doubt that the right decision will depend on the ratio of the two deltas?
There’s really nothing to see here. .This is just another case of generating paradoxes in probability theory when you don’t do a full analysis using finite, non zero probability assignments.
This is a similar issue the OP has come up against. Proposition1 is that A obeys certain game theoretic rules. Proposition2 is the report that implicates A violating those rules. When your propositions seem mutually contradictory, because you have lazily assigned 0 probability to them, hilarity ensues. Assign finite values, and the mysteries are resolved.
You are basically using the trembling hand equilibrium concept. I picked the payoffs so this would not yield an easy solution. Consider an equilibrium where Player 1 intends to pick A, but there is a small but equal chance he will pick B or C by mistake. In this equilibrium Player 2 would pick Y if he got to move, but then Player 1 would always intend to Pick C, effectively pretending he had made a mistake.