Maybe try this one? Let me know if that helps or if you’re looking for something different.
The complete class theorem states, informally: any Pareto optimal decision rule is a Bayesian decision rule (i.e. it can be obtained by choosing some prior, observing data, and then maximizing expected utility relative to the posterior).
Roughly, the argument is that if I have a collection W of possible worlds that I could be in, and a value U(w) to taking a particular action in world w, then any Pareto optimal strategy implicitly assigns an “importance” p(w) to each world, and takes the action that maximizes the sum of p(w)*U(w). We can then show that this is equivalent to using the Bayesian decision rule with p(w) as the prior over W. The main thing needed to formalize this argument is the separating hyperplane theorem, which is what the linked paper does.
Does the complete class theorem thus provide what Peterson (2004) and Easwaran (unpublished) think is missing in classical axiomatic decision theory: namely, a justification for choosing a prior, observing data, and then maximizing expected utility relative to the posterior?
Maybe try this one? Let me know if that helps or if you’re looking for something different.
The complete class theorem states, informally: any Pareto optimal decision rule is a Bayesian decision rule (i.e. it can be obtained by choosing some prior, observing data, and then maximizing expected utility relative to the posterior).
Roughly, the argument is that if I have a collection W of possible worlds that I could be in, and a value U(w) to taking a particular action in world w, then any Pareto optimal strategy implicitly assigns an “importance” p(w) to each world, and takes the action that maximizes the sum of p(w)*U(w). We can then show that this is equivalent to using the Bayesian decision rule with p(w) as the prior over W. The main thing needed to formalize this argument is the separating hyperplane theorem, which is what the linked paper does.
Does the complete class theorem thus provide what Peterson (2004) and Easwaran (unpublished) think is missing in classical axiomatic decision theory: namely, a justification for choosing a prior, observing data, and then maximizing expected utility relative to the posterior?