Does Logical Decision Theories actually give meaningfully better recommendations on real world problems, particularly voting, frequently referenced?
One of the main reasons given for preferring logical decision theories (LDT), or particularly functional decision theory (FDT) is that agents do better in real world problems. Indeed, the article here on logical decision theory opens by discussing voting. I recently posted a discussion of a hypothetical where FDT agents perform worse, but I think when applying it in practice to the real world case of voting which is often given as a preference is actually better (see here for Eliezer Yudkowsky's discussion of voting under decision theories where he argues for logical decision theory being better). Particularly, I think that for most people this discussion gets wrong what causal decision theory actually would recommend.
To begin (note, I spend a while going over how to model voting decisions and different utility to CDT modeling of decisions for a few paragraphs, and later discuss practical agent to agent comparisons), let us imagine what the expected utility is for an agent under CDT of voting in some election. Let's say there are two candidates, like Yudkowsky, I will use the Simpson's Kang and Kodos. If Kang wins, we have some expected outcome (O1), if Kodos wins we have some expected outcome (O2). Let's say our agent is a Kang supporter and has a positive evaluation of O1 such that O1>O2.[1]
Our agent is evaluating the value of voting for Kang (A1) or not voting (A0).
In the simplest case, with no externalities an EDT agent would say: "we should vote if our evidential evidence indicates voting is more likely to lead to Kang winning" (i.e., if P(O1|A1)>P(O1|A0). A CDT agent would say "we should vote if there is a positive probability that our vote will cause Kang to win" (we can say this works out equivalently, if P(O1|A1)>P(O1|A0) we should vote).
If we are a simplistic agent, in both cases we should vote, as in