Voting Theory
The study of procedures for aggregating individual preferences into a collective decision.
Definition
A voting rule maps each profile of ranked or scored preferences over alternatives to a winner. Common rules: plurality, Borda count, instant-runoff (IRV), approval voting, Condorcet methods.
Key evaluation criteria: Pareto efficiency, Condorcet consistency, independence of irrelevant alternatives (IIA), strategy-proofness.
Intuition
No voting rule is perfect — Arrow's theorem shows any reasonable rule must violate at least one basic desideratum.
Different rules can produce wildly different outcomes from the same preferences, so the choice of rule is itself a political decision.
Worked example
In the 2000 US presidential election, third-party candidate Ralph Nader split the vote, illustrating spoiler effects in plurality voting.
Borda count assigns points by rank position; it's used in Eurovision and some academic elections.
The math
Arrow (1951): no social welfare function for alternatives simultaneously satisfies unrestricted domain, Pareto efficiency, IIA, and non-dictatorship.
The Gibbard-Satterthwaite theorem: every non-dictatorial voting rule with alternatives is manipulable (not strategy-proof).
Where it is used
Political elections, committee decision-making, collaborative filtering, and multi-agent preference aggregation.
Foundational in social choice theory and political science.
More in Game theory
Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.