Set theory: Difference between revisions
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Many voting method criteria can be thought of in terms of sets. For example, the [[Unanimity criterion|unanimity criterion]] requires that if between two candidates, all voters prefer the former over the latter, then the latter candidate must not win; this can be interpreted in set theory (when solely looking at the winner(s) of the election) as "the winner set selected by a voting method must always be a subset of the largest "unanimity-compliant" set of candidates such that there is no candidate who is unanimously preferred over one of the candidates in the unanimity-compliant set."
In the context of ranked methods, several sets have been proposed for the purposes of identifying which candidates or groups of candidates are better than others. One of the most notable of these is the [[Smith set]]. Note that several set-related criteria can be thought of as requiring the election of a candidate from a smallest set of candidates meeting some requirement, because though there may be several sets meeting that requirement, only the smallest of these sets (supposing all of the sets are nested) ensures that the voting method elected someone in every possible set meeting the requirement.
Some criteria dealing with sets are:
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'''Superset''': If one set has every element that another set has, then it is a superset.
'''Singleton''': A set with exactly one alternative in it.
'''Singleton''': A set with exactly one alternative in it.<blockquote>An '''inclusion-wise maximal set''' among a collection of sets is a set that is not a subset of some other set in the collection. An '''inclusion-wise minimal set''' among a collection of sets is a set in the collection that is not a superset of any other set in the collection.</blockquote>▼
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== Condorcet ==
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