Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures (social welfare functions) used to combine individual preferences into a coherent whole. It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory.

Real-world examples of social choice rules include constitutions and parliamentary procedures for voting on laws, as well as electoral systems; as such, the field is occasionally called voting theory. It is closely related to mechanism design, which uses game theory to model social choice with imperfect information and self-interested citizens.

Social choice differs from decision theory in that the latter is concerned with how individuals, rather than societies, can make rational decisions.

The earliest work on social choice theory comes from the writings of the Marquis de Condorcet, who formulated several key results including his jury theorem and his example showing the impossibility of majority rule. His work was prefigured by Ramon Llull's 1299 manuscript Ars Electionis (The Art of Elections), which discussed many of the same concepts, but was lost in the Late Middle Ages and only rediscovered in the early 21st century.

Kenneth Arrow's book Social Choice and Individual Values is often recognized as inaugurating the modern era of social choice theory. Later work has also considered approaches to legal compensation, fair division, variable populations,^{[citation needed]} partial strategy-proofing of social-choice mechanisms, natural resources, capabilities and functionings approaches, and measures of welfare.

Arrow's impossibility theorem is a key result showing that social choice functions based only on ordinal comparisons, rather than cardinal utility, will behave incoherently (unless they are dictatorial). Such systems violate independence of irrelevant alternatives, meaning they suffer from spoiler effects—the system can behave erratically in response to changes in the quality or popularity of one of the options.

Condorcet's example demonstrates that democracy cannot be thought of as being the same as simple majority rule or majoritarianism; otherwise, it will be self-contradictory when three or more options are available. Majority rule can create cycles that violate the transitive property: Attempting to use majority rule as a social choice function creates situations where we have A better than B and B better than C, but C is also better than A.

This contrasts with May's theorem, which shows that simple majority is the optimal voting mechanism when there are only two outcomes, and only ordinal preferences are allowed.