The Independence of Irrelevant Alternatives (IIA) is a principle in decision theory and social choice theory which states that the relative ranking of two options should not be affected by the introduction or removal of additional alternatives. Violations of IIA can lead to paradoxes and inconsistencies in collective decision-making processes, as demonstrated by Arrow's Impossibility Theorem.

Independence Of Irrelevant Alternatives

Independence of Irrelevant Alternatives

principle in decision theory

Social Choice Theory explores how individual preferences can be aggregated to reach a collective decision, addressing the challenges of fairness, efficiency, and representation. It encompasses various voting systems and decision-making processes, highlighting the potential for paradoxes and inconsistencies, such as those identified by Arrow's Impossibility Theorem.

social choice theory

relative ranking of two options

introduction or removal of additional alternatives

Violations of IIA

Paradoxes in decision-making

inconsistencies in collective decision-making processes

Arrow's Impossibility Theorem demonstrates that no rank-order voting system can convert individual preferences into a community-wide ranking while simultaneously meeting a set of fair criteria, including unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. This theorem reveals inherent limitations in designing a perfect voting system, highlighting the trade-offs necessary in collective decision-making processes.

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