Decision theory solves the extremely hard* problem of telling you what you should do if you have a consistent and mathematically formalized model of the world and a utility function telling you exactly how good any particular world-state is. The most common decision theories are evidential decision theory and causal decision theory; various [[accursed decision theories]] exist but are not in wide use.
EDT says, informally, that you should take whatever action has the highest expected utility (i.e. the sum of utility for each outcome weighted by the probability of that outcome conditional on you taking the action).
Informally, CDT says that you should take whatever action //causes// the highest expected utility, i.e. the conditional probability is replaced with a counterfactual (there is some debate about how to operationalize this, but roughly speaking, it's the probability if you replaced the action you took with another one).
== Limitations
Neither theory provides a satisfying answer to all problems.
