I think if you fully specify the model (including the reasons for commitment rather than just delaying the decision in the first place), you’ll find that the reason for committing is NOT about updates, but about adversarial game theory. Specifically, include in your model that if facing a NORMAL opponent, failure to commit turns your (D, S) outcome (+1) into a (S, D) (-1), because the normal opponent will dare if you haven’t committed, and then you are best off swerving. You’ve LOST VALUE because you gave too much weight to the crazy opponent.
How your (distribution of) opponents react to your strategy, which is conditional on your beliefs about THEIR strategy is the core of game theory. If you have a mix of crazy opponents and rational opponents who you think haven’t committed yet, you don’t need to introduce any update mechanisms, you just need your current probability estimates about the distribution, and commit or don’t based on maximizing your EV.
Where the conservation of expected evidence comes in is that you CANNOT expect to increase your chances of facing a crazy opponent. If you did expect that, you actually have a different prior than you think.
The model is fully specified (again, sorry if this isn’t clear from the post). And in the model we can make perfectly precise the idea of an agent re-assessing their commitments from the perspective of a more-aware prior. Such an agent would disagree that they have lost value by revising their policy. Again, I’m not sure exactly where you are disagreeing with this. (You say something about giving too much weight to a crazy opponent — I’m not sure what “too much” means here.)
Re: conservation of expected evidence, the EA-OMU agent doesn’t expect to increase their chances of facing a crazy opponent. Indeed, they aren’t even aware of the possibility of crazy opponents at the beginning of the game, so I’m not sure what that would mean. (They may be aware that their awareness might grow in the future, but this doesn’t mean they expect their assessments of the expected value of different policies to change.) Maybe you misunderstand what we mean by “unawareness”?
The missing part is the ACTUAL distribution of normal vs crazy opponents (note that “crazy” is perfectly interchangeable with “normal, who was able to commit first”), and the loss that comes from failing to commit against a normal opponent. Or the reasoning that a normal opponent will see it as commitment, even when it’s not truly a commitment if the opponent turns out to be crazy.
Anyway, interesting discussion. I’m not certain I understand where we differ on it’s applicability, but I think we’ve hashed it out as much as possible. I’ll continue reading and thinking—feel free to respond or rebut, but I’m unlikely to comment further. Thanks!
I think if you fully specify the model (including the reasons for commitment rather than just delaying the decision in the first place), you’ll find that the reason for committing is NOT about updates, but about adversarial game theory. Specifically, include in your model that if facing a NORMAL opponent, failure to commit turns your (D, S) outcome (+1) into a (S, D) (-1), because the normal opponent will dare if you haven’t committed, and then you are best off swerving. You’ve LOST VALUE because you gave too much weight to the crazy opponent.
How your (distribution of) opponents react to your strategy, which is conditional on your beliefs about THEIR strategy is the core of game theory. If you have a mix of crazy opponents and rational opponents who you think haven’t committed yet, you don’t need to introduce any update mechanisms, you just need your current probability estimates about the distribution, and commit or don’t based on maximizing your EV.
Where the conservation of expected evidence comes in is that you CANNOT expect to increase your chances of facing a crazy opponent. If you did expect that, you actually have a different prior than you think.
The model is fully specified (again, sorry if this isn’t clear from the post). And in the model we can make perfectly precise the idea of an agent re-assessing their commitments from the perspective of a more-aware prior. Such an agent would disagree that they have lost value by revising their policy. Again, I’m not sure exactly where you are disagreeing with this. (You say something about giving too much weight to a crazy opponent — I’m not sure what “too much” means here.)
Re: conservation of expected evidence, the EA-OMU agent doesn’t expect to increase their chances of facing a crazy opponent. Indeed, they aren’t even aware of the possibility of crazy opponents at the beginning of the game, so I’m not sure what that would mean. (They may be aware that their awareness might grow in the future, but this doesn’t mean they expect their assessments of the expected value of different policies to change.) Maybe you misunderstand what we mean by “unawareness”?
The missing part is the ACTUAL distribution of normal vs crazy opponents (note that “crazy” is perfectly interchangeable with “normal, who was able to commit first”), and the loss that comes from failing to commit against a normal opponent. Or the reasoning that a normal opponent will see it as commitment, even when it’s not truly a commitment if the opponent turns out to be crazy.
Anyway, interesting discussion. I’m not certain I understand where we differ on it’s applicability, but I think we’ve hashed it out as much as possible. I’ll continue reading and thinking—feel free to respond or rebut, but I’m unlikely to comment further. Thanks!