You could always choose to manage ignorance by choosing a prior. It's not obvious whether you should. But as it turns out, we have results like the complete class theorem, which imply that EU maximization with respect to an appropriate prior is the only "Pareto efficient" decision procedure (any other decision can be changed so as to achieve a higher reward in every possible world).
This analysis breaks down in the presence of computational limitations; in that case it's not clear that a "rational" agent should have even an implicit representation of a distribution over possible worlds (such a distribution may be prohibitively expensive to reason about, much less integrate exactly over), so maybe a rational agent should invoke some decision rule other than EU maximization.
The situation is sort of analogous to defining a social welfare function. One approach is to take a VNM utility function for each individual and then maximize total utility. At face value it's not obvious if this is the right thing to do--choosing an exchange rate between person A's preferences and person B's preferences feels pretty arbitrary and potentially destructive (just like choosing prior odds between possible world A and possible world B). But as it turns out, if you do anything else then you could have been better off by picking some particular exchange rate and using it consistently (again, modulo practical limitations).
as it turns out, we have results like the complete class theorem, which imply that EU maximization with respect to an appropriate prior is the only "Pareto efficient" decision procedure (any other decision can be changed so as to achieve a higher reward in every possible world).
I found several books which give technical coverage of statistical decision theory, complete classes, and admissibility rules (Berger 1985; Robert 2001; Jaynes 2003; Liese & Miescke 2010), but I didn't find any clear explanation of exactly how the complete class the...
Previously: round 1, round 2, round 3
From the original thread:
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