An Introduction to Decision Theory

by Martin Peterson


good overview. imo not enough thought was put into why the distinctions made are appropriate and/or natural, as opposed to clean, and it shied away from some of the more interesting math. still a decent reference if you want to learn a bunch of vocab and/or concepts in an evening.

he mentions that he doesn’t find the Dutch book criterion a satisfying justification of why an agent should use subjective probabilities which satisfy the probability axioms. this is probably true? but the concept of a ‘Dutch book’ generalizes far beyond coherence in this sense, it can also be relaxed to guarantee logical coherence in a practical sense (Garrabrant et. al. prove that a form of a Dutch book criterion is enough to guarantee nearly all desiderata for reasoning under uncertainty except for Gaifman induction). as for the philosophical justification of translating utilities into money, it’s plausible we’re packaging a lot of hidden assumptions here? but i don’t really know what they are. i should probably think about this

again with the insistence on the absolute divide between ordinal and cardinal utilities!! i argue that, in practice, in the scenarios we care about, they’re essentially isomorphic, and that all a reasoner needs is some ordinal utility function / ordering over world states. yes, maybe your environment is countable / discrete and not uncountable / continuous, but even then you can still make a natural mapping and aggregate preferences decently.

also, the book argues against EDT on the basis that an EDT agent can’t naturally ascribe probabilities to their own beliefs if it results in epicycles? this is mostly just incorrect (or, there are sane ways of dealing with this), but it is something to worry about, sure. there are much better arguments against EDT (like the Smoking Lesion: this is a good descriptor here)

chapters 11-14 are good and short overviews of game theory & social choice theory that are well worth it. you quickly get exposed to ~all the major game theoretic settings, as well as stuff like Arrow’s impossibility results / Harsanyi’s utilitarian theorem(s?). if i had read this part six months ago I’d be in a much better place I think