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by Jessica Taylor 610 days ago | link | parent

I still don’t understand why the expected utility is \(-W\) rather than \(1/2\).



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 \(-W\).

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by Patrick LaVictoire 599 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.

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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 \(Q\).

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