The Entangled Dimensions of Decision Theory

TL;DR. LessWrong's decision-theory debates (Newcomb, FDT vs CDT, counterfactual muggings) are almost entirely about what we suppose when we consider a candidate action or policy . There is a second, older, semi-orthogonal, but not fully orthogonal question: how to score a gamble once you know the possible outcomes . The predominant (and mostly implicit) answer to that was "take the expected utility". This post treats the two questions, plus a question about how a choice made before receiving information should relate to choices made afterward, as separate axes, and maps every decision theory you have heard of (and several nobody has built) into the resulting grid. Interestingly, the axes are provably entangled : theorems old and new show that there exist different restrictions on what places in that "decision-theoretic space" are inhabitable. I think there is a structure, maybe a deep and consequential structure, inside this map of decision theories which shows what possible combinations across the axes are coherent and fruitful. If we study it, we may understand the entire set of all possible coherent decision theories, something akin to the "metatheory of decision theories". It may be useful to know the entire set. This is both a self-educational note and a research post. I have tried to state the scope of every result. While I am not certain about every conclusion about the "space of decision theories," I am confident that thinking in terms of the proposed space is useful…