Thanks Dagon:
Any mechanism to revoke or change a commitment is directly giving up value IN THE COMMON FORMULATION of the problem
Can you say more about what you mean by “giving up value”?
Our contention is that the ex-ante open-minded agent is not giving up (expected) value, in the relevant sense, when they “revoke their commitment” upon becoming aware of certain possible counterpart types. That is, they are choosing the course of action that would have been optimal according to the priors that they believe they should have set at the outset of the decision problem, had they been aware of everything they are aware of now. This captures an attractive form of deference — at the time it goes updateless / chooses its commitments, such an agent recognizes its lack of full awareness and defers to a version of itself that is aware of more considerations relevant to the decision problem.
As we say, the agent does make themselves exploitable in this way (and so “gives up value” to exploiters, with some probability). But they are still optimizing the right notion of expected value, in our opinion.
So I’d be interested to know what, more specifically, your disagreement with this perspective is. E.g., we briefly discuss a couple of alternatives (close-mindedness and awareness growth-unexploitable open-mindedness). If you think one of those is preferable I’d be keen to know why!
This model doesn’t seem to really specify the full ruleset that it’s optimizing for
Sorry that this isn’t clear from the post. I’m not sure which parts were unclear, but in brief: It’s a sequential game of Chicken in which the “predictor” moves first; the predictor can fully simulate the “agent’s” policy; there are two possible types of predictor (Normal, who best-responds to their prediction, and Crazy, who Dares no matter what); and the agent starts off unaware of the possibility of Crazy predictors, and only becomes aware of the possibility of Crazy types when they see the predictor Dare.
If a lack of clarity here is still causing confusion, maybe I can try to clarify further.
I also suspect you’re conflating updates of knowledge with strength and trustworthiness of commitment. It’s absolutely possible (and likely, in some formulations about timing and consistency) that a player can rationally make a commitment, and then later regret it, WITHOUT preferring at the time of commitment not to commit.
I’m not sure I understand your first sentence. I agree with the second sentence.
For one thing, we’re calling such agents “Crazy” in our example, but they need not be irrational. They might have weird preferences such that Dare is a dominant strategy. And as we say in a footnote, we might more realistically imagine more complex bargaining games, with agents who have (rationally) made commitments on the basis of as-yet unconceived of fairness principles, for example. An analogous discussion would apply to them.
But in any case, it seems like the theory should handle the possibility of irrational agents, too.
Here’s what I think you are saying: In addition to giving prior mass to the hypothesis that her counterpart is Normal, Alice can give prior mass to a catchall that says “the specific hypotheses I’ve thought of are all wrong”. Depending on the utilities she assigns to different policies given that the catchall is true, then she might not commit to Dare after all.
I agree that Alice can and should include a catchall in her reasoning, and that this could reduce the risk of bad commitments. But that doesn’t quite address the problem we are interested in here. There is still a question of what Alice should do once she becomes aware of the specific hypothesis that the predictor is Crazy. She could continue to evaluate her commitments from the perspective of her less-aware self, or she could do the ex-ante open-minded thing and evaluate commitments from the priors she should have had, had she been aware of the things she’s aware of now. These two approaches come apart in some cases, and we think that the latter is better.
I don’t see why EA-OMU agents should violate conservation of expected evidence (well, the version of the principle that is defined for the dynamic awareness setting).