Independence of irrelevant alternatives: Difference between revisions
Independence of irrelevant alternatives (view source)
Revision as of 15:23, 25 November 2021
, 2 years agoChange links to "independence of" criteria as these now exist. In addition, rephrase reference to CES example of min-max voting.
(Import rock-paper-scissors example of IIA failure from Wikipedia. Add reference to River and Ranked Pairs in ISDA/IPDA section) |
(Change links to "independence of" criteria as these now exist. In addition, rephrase reference to CES example of min-max voting.) |
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To mitigate the reach of IIA failures, less strict properties have been proposed (some of which are incompatible with IIA):
* '''[[Independence of Smith-dominated Alternatives|Independence of Smith-dominated alternatives]]''' (ISDA) and '''[[
* '''[[
* '''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.
* Woodall's '''Weak IIA''': If x is elected, and one adds a new calternative y ahead of x on some of the ballots on which x was first preference (and nowhere else), then either x or y should be elected.
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* A candidate can enter or drop out of the election without changing the result (unless they win in one of the cases).
The second implication is strongly disputed for voting methods that pass IIA. It requires assuming voters won't change their preferences when the set of alternatives expands or contracts; with something like [[Score voting]], this means no voters can do [[normalization]]. A commonly used example is that if a candidate that a voter finds terrible enters the race, and is likely to win, then the voter has an incentive to do [[Min-max voting]].
=== Strategic implications ===
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* [[Vote splitting]]
* [[w:Gibbard's theorem]]
==References==
<references/>
[[Category:Voting system criteria]]
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