Independence of irrelevant alternatives: Difference between revisions
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Adding irrelevant (non-winning) candidates should not be able to change the election results. The only time when adding candidates can change the election results is when they change the election result to one in which they are one of the winners. |
Adding irrelevant (non-winning) candidates should not be able to change the election results. The only time when adding candidates can change the election results is when they change the election result to one in which they are one of the winners. |
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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). |
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| ⚫ | [[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. |
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| ⚫ | [[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. |
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[[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. |
[[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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Therefore, less strict properties have been proposed (some of which are incompatible with IIA): |
Therefore, less strict properties have been proposed (some of which are incompatible with IIA): |
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* '''[[Independence of Smith-dominated Alternatives|Independence of Smith-dominated alternatives]]''' (ISDA) |
* '''[[Independence of Smith-dominated Alternatives|Independence of Smith-dominated alternatives]]''' (ISDA) and '''[[Uncovered set|Independence of covered alternatives]]''' |
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* '''[[Uncovered set|Independence of covered alternatives]]''' |
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* '''[[Pareto criterion|Independence of Pareto-dominated alternatives]]''' (IPDA) |
* '''[[Pareto criterion|Independence of Pareto-dominated alternatives]]''' (IPDA) |
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* '''Local independence of irrelevant alternatives''' (LIIA), which says that if the alternative ranked first or last in the outcome is removed, the relative ordering of the other alternatives in the outcome must not change. [[Kemeny-Young]] and [[Ranked Pairs]] satisfies this criterion, but the [[Schulze method]] does not. |
* '''Local independence of irrelevant alternatives''' (LIIA), which says that if the alternative ranked first or last in the outcome is removed, the relative ordering of the other alternatives in the outcome must not change. [[Kemeny-Young]] and [[Ranked Pairs]] satisfies this criterion, but the [[Schulze method]] does not. |
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