Decision theory confuses me. On one hand, evidential decision theory is obviously wrong. On the other hand, causal decision theory is obviously applied incorrectly.

Evidential decision theory is wrong since it conditions on the act made. One reason why you shouldn’t do this is that this presupposes that your act is a random variable, itself strange, but it’s also conceptually wrong. Decision theory is about making choices, in most cases making a choice between random variables.

Causal decision theory has its own share of problems. First, it is presented in a far too complicated way, and too much emphasis is placed on causality. This has forced hundreds of authors to employ difficult theories such as Lewis’ theory of counterfactuals or Pearl’s causal diagrams to say something about decision theory. As it turns out, this is completely unnecessary and has probably contributed its fair share to the current confusion about decision theory. Second, the idea that everything should be causal makes people read too much into it, forcing a problem to causal even when it is impossible (Newcomb’s problem, I’m looking at you!)

Basic decision theory, neither evidential or causal, is surprisingly simple to formulate. You have a family of stochastic variables \(Y_x\), and you can choose between them using your choice \(x\). The utility of one particular outcome of \(Y_x,x\) is captured by a utility function \(u(Y_x,x)\), and you want to maximize the expected utility \(Eu(Y_x,x)\).

This framework is strong enough for most problems. It must probably be modified to account for dynamic decision problems, optimal stopping, and some of the stranger decision problems in the literature. But most of these modifications aren’t that difficult.