by Jessica Taylor 611 days ago | link | parent I’m not sure what the “arbitrarily bad decisions” example is meant to illustrate? If the 2 agents randomize uniformly between r and l, they each get an expected utility of 1/2, which is greater than -1.

 by Stuart Armstrong 611 days ago | link But there aren’t two players, that’s just the model. What I mean is that all these ways of factoring out B can lead to arbitrary bad real expected utility, as compared with the agent that doesn’t factor. reply
 by Jessica Taylor 610 days ago | link I still don’t understand why the expected utility is $$-W$$ rather than $$1/2$$. reply
 by Stuart Armstrong 610 days ago | link In the real world, the utility is given by the diagonal (since $$a$$ and $$a'$$ being different in $$Q(a,a')$$ is the fiction allowing for factoring of $$B$$). Therefore the genuine expected utilities are only on the diagonal, and anything else than $$c$$ will give $$-W$$. reply
 by Patrick LaVictoire 598 days ago | link There’s nothing in the setup preventing the players from having access to independent random bits, though it’s fair to say that these approaches assume this to be the case even when it’s not. But then the fault is with that assumption of access to randomness, not with any of the constraints on $$Q$$. So I don’t think this is a strike against these methods. reply
 by Stuart Armstrong 597 days ago | link I’m not following. This “game” isn’t a real game. There are not multiple players. There is one agent, where we have taken its real, one-valued probability, and changed it into a two-valued $$Q$$, for the purposes of factoring out the impact of the variable. The real probability is the original probability, which is the diagonal of $$Q$$. reply

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