Definition
Decision theory is the systematic study of rational choice under uncertainty. It asks what an agent ought to do when the consequences of each available action depend on circumstances the agent cannot fully control or foresee.
A decision problem has three parts: the set of actions you can take, the set of possible states of the world, and the outcome that each action-and-state pair produces. Decision theory supplies a rule for ranking the actions given how good each outcome is and how likely each state is.
Why it matters
How it works
The dominant criterion is to choose the action with the highest expected utility: weight the value of each possible outcome by the probability of the state that brings it about, sum the results, and pick the largest total. This balances desirability against likelihood in a single number.
Priest stresses that decision theory inherits all the difficulties of probability — interpreting the numbers, fixing them in the first place — and adds new puzzles of its own. The Newcomb problem in particular sets the expected-utility rule against a rival principle of dominance, and the two give opposite advice. Decision theory is therefore not a finished science but an active argument about what rationality demands.