Independence of irrelevant alternatives: Difference between revisions
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Any voting method which passes the [[Majority criterion|majority criterion]] in the two-candidate case will fail IIA, because of the [[Condorcet paradox]]. Certain voting methods only do so when all voters are strategic (i.e. [[Approval voting]], [[Score voting]], and [[Majority Judgment]]); they are guaranteed to fail IIA under those particular circumstances (i.e. when all voters are strategic).
[[Condorcet method]]s necessarily fail this criterion, although some, such as [[Ranked Pairs]], satisfy a related but weaker criterion known as [[local independence of irrelevant alternatives]]. [[Borda count]], [[Coombs' method]], and [[Instant-runoff voting]] fail.
[[Range voting]], [[approval voting]], and [[majority judgment]] satisfy the criterion if the voters grade or rate the candidates on an absolute scale that doesn't depend on who is in the running. Note that this means no voter can [[Normalization|normalize]] their ballot, and so in a two-candidate election the majority can't vote strategically to make their preferred candidate win.
[[Arrow's impossibility theorem]] states that no voting system can satisfy universal domain, non-imposition, non-dictatorship, unanimity, and independence of irrelevant alternatives. Since universal domain implies that the method is an ordinal method, the impossibility theorem only applies to [[ordinal voting]]. In practice, this means that no deterministic ranked ballot system can satisfy independence of irrelevant alternatives without either having a dictator (whose ballot decides who wins no matter the other ballots), failing to elect a candidate that the whole electorate ranks first, or rendering one or more outcomes impossible no matter the ballots.
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