Social choice theory studies how individual preferences determine a collective decision. A social choice function selects one alternative from a preference profile; strategyproofness asks whether agents can benefit by misrepresenting their preferences.
A deterministic social choice function maps profiles of preference orders to single alternatives. Unrestricted domain permits every profile in ; onto means every alternative lies in the range. A unanimous rule selects an alternative whenever every agent ranks it first.
With an odd number of agents and two alternatives, select the alternative ranked first by a strict majority. The rule is onto, strategyproof, and for at least three agents has no dictator in social choice. A pivotal agent already gets its preferred alternative by reporting truthfully; a nonpivotal agent cannot change the outcome alone.
A dictatorship always selects the top alternative of one fixed agent . Other agents cannot alter the selection against that agent's preference. This is the social-choice meaning of dictatorship, rather than a political classification.
A dictator is the fixed agent whose top-ranked alternative is always selected by a dictatorship in social choice.
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Social choice theory is a theoretical framework that explores how individuals' preferences can be aggregated to make collective decisions. It encompasses a variety of methods and principles for assessing and determining the best course of action in situations where multiple individuals have differing preferences, needs, or choices. Key aspects of social choice theory include: 1. **Voting Systems**: The study of various electoral systems and how they influence the outcomes of elections. This includes methods such as plurality voting, ranked-choice voting, and others.