Decision theory is the study of rational decision-making under conditions of empirical uncertainty.
Decision theory is normative: it provides us with a means of assessing decisions, and guidance on how to make the best decisions. The goal is not necessarily to show how real-life agents actually make decisions, which is explored in behavioral economics and the psychology of decision making.
Suppose that a person has more than one action available to them, that they are uncertain about the state of the world, and that they know that different outcomes will result from their action depending on what the true state of the world is. Even once they have assigned values to each of these outcomes, they will need a function to process those value-assigned outcomes to the actions available to them: one that can rank the actions by how good they are. For example, if they think that they should maximize expected value, then the function will rank all of the actions available to them by the amount of value that each of them is expected to produce.
Further reading
Steele, Katie and H. Orri Stefánsson (2020), Decision Theory, The Stanford Encyclopedia of Philosophy.
Peterson, Martin (2017) An Introduction to Decision Theory, 2nd ed., Cambridge: Cambridge University Press.
Oesterheld, Caspar (2017) A comprehensive list of decision theories, The Universe from an Intentional Stance, June 22.
Related entries
alternatives to expected value theory | altruistic wager | credence | decision theoretic uncertainty | economics | game theory | risk aversion | sequence vs. cluster thinking