Independence of irrelevant alternatives: Difference between revisions
Independence of irrelevant alternatives (view source)
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(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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=== Cardinal methods ===
[[Range voting]], [[approval voting]], and [[majority judgment]] satisfy the criterion. This implies that if
Note, however, that this means no voter can [[Normalization|normalize]] their ballot. This also requires voters not to vote strategically (which can cause majority failures).
=== Ranked methods ===
[[Arrow's impossibility theorem]] states that no [[ordinal voting]] system
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Let's say that we have a majoritarian ranked ballot method, i.e. one that elects the candidate with a majority of the vote (if there are only 2 candidates). With an election that's a Condorcet cycle (rock-paper-scissors situation), like this:
{{ballots|
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35: C>A>B}}
at least one of A, B or C must be elected (or have a chance of winning the election if the method is nondeterministic). There are
*Case 1: ''A'' is elected. IIA is violated because the 75% who prefer ''C'' over ''A'' would elect ''C'' if ''B'' were not a candidate.
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*Case 3: ''C'' is elected. IIA is violated because the 65% who prefer ''B'' over ''C'' would elect ''B'' if ''A'' were not a candidate.
No matter who wins, the method
== Related criteria ==
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)
* '''[[Independence of covered alternatives]]'''
* '''[[Independence of Pareto-dominated alternatives]]''' (IPDA)
* '''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
* Woodall's '''Weak IIA''': If
Neither the [[Borda count]], [[Coombs' method]] nor [[Instant-runoff voting]] satisfies the less strict criteria above. [[Ranked Pairs]]
== Anecdote ==
An anecdote which illustrates a violation of this property has been attributed to Sidney Morgenbesser:
<blockquote>After finishing dinner, Sidney Morgenbesser decides to order dessert.
== Implications ==
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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
=== Strategic implications ===
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