Decision theory

Decision theory studies how choices are made or should be made by evaluating available actions, preferences, outcomes, and uncertainty.

Utility: A numerical representation of how desirable an outcome is to an agent. Utility gives decision theory a way to compare outcomes by preference.
Expected utility hypothesis: The principle that rational choices under uncertainty can be represented as maximizing expected utility. It gives a central rule for choosing among probabilistic consequences.
Normative decision theory: The study of principles for making choices that satisfy standards of rationality or optimality. It asks how choices should be made, rather than merely describing them.
Game theory: The mathematical study of strategic interaction among decision-makers whose outcomes depend on one another's actions. It extends choice analysis to situations where others also choose.
Daniel Bernoulli: An eighteenth-century mathematician who introduced diminishing marginal utility to explain choices under risk. His analysis of the St. Petersburg paradox anticipated utility-based choice.
Preference relation: A relation that represents how an agent ranks alternatives or outcomes. Preferences determine which outcomes count as better for a decision-maker.
Bayesian decision theory: A framework combining probability, utility, and available actions to select decisions under uncertainty. It makes explicit how beliefs and values jointly determine an action.
Descriptive decision theory: The empirical study of how people actually make choices. It examines real behavior that can depart from formal rational models.
Medical decision-making: The process of selecting healthcare actions by weighing evidence, benefits, harms, and patient preferences. Clinical choices combine uncertain outcomes with differing patient values.
St. Petersburg paradox: A gambling problem whose infinite expected monetary payoff conflicts with finite willingness to pay. It exposed the limits of evaluating risky choices by expected money alone.

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