I was in Austin a couple weeks ago for the second Texas Decision Theory Workshop, which was a lot of fun. It was a fairly small group, and some interesting topics I didn’t know much about were discussed. In particular, there was a lot of discussion (primarily by Sahotra Sarkar and Carl Wagner) about decision making with imprecise probabilities. There was also a lot of discussion of multiple-criteria decision making. My friend Alex Moffett discussed the impossibility theorems of Arrow, and Gibbard and Satterthwaite – he mentioned an analogy between multiple-agent decision making (as in the traditional presentations of these theorems) and multiple-criteria decision making, suggesting that in this context at least, the “independence of irrelevant alternatives” criterion really is important. And Mike Titelbaum presented some of his work on generalized versions of conditionalization as constraints on rational agents even under forgetting.
I talked about some of the things I discussed earlier this summer, but with more of a worked-out formalism for describing the decision apparatus (and constructing stronger decision theories out of weaker ones). I was surprised to see that some of this formalism that I developed for infinitary cases seems to resemble some of the formalisms for imprecise probabilities! I’ll have to look into this more to see how they really connect.