Summability criterion: Difference between revisions
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{{ambox|text=An article titled "[[wikipedia:Summability criterion|Summability criterion]]" was deleted from [[English Wikipedia]] in 2009.<ref>[[English Wikipedia]] AfD for "Summability Criterion": https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Summability_criterion</ref> Before the page was deleted from Wikipedia, it was copied to [[Electowiki]]. Those with the correct permissions can see the edit history.<ref>Edit history for "Summability criterion" on English Wikipedia: https://en.wikipedia.org/w/index.php?title=Summability_criterion&action=history</ref>}}
The [[summability criterion]] is a [[voting system criterion]], used to objectively compare [[voting system]]s. The criterion states:<blockquote><em>Each vote should be able to be mapped onto a summable array, such that its size at most grows polynomially with respect to the amount of candidates, the summation operation is associative and commutative and the winner could be determined from the array sum for all votes cast alone.</em></blockquote>Note that the blockquote above was copied to [[electowiki]] before it was deleted. There were other changes made to this article after it was copied to [[Summability criterion (Wikipedia version)]].<ref name=":0">The text above is derived from text that was deleted from [[English Wikipedia]] in 2009. See the edit history for the old page for authorship before 2009or the edit history of [[Summability criterion (Wikipedia version)]] on this wiki.</ref>
== Compliance ==
According to a deleted Wikipedia article<ref name=":0" />, the following methods comply with the summability criterion:
* [[Majority Choice Approval]]
* [[Schulze method]]
* [[Approval voting]]
* [[Range voting]]
* [[Borda count]]
* [[Borda count|Nanson's method]]
* [[Plurality voting]]
According to that same Wikipedia article (and to William Poundstone's book ''[[Gaming the Vote]]''), [[Instant-Runoff Voting]] does not comply.<ref>''Gaming the Vote, Why Elections Aren't Fair (and What We Can Do About It),'' William Poundstone, New York: Hill and Wang, 2008, p. 170.</ref>
'''Summability of various methods'''▼
In [[plurality voting]], the number of ballots for each candidate may be counted, and these totals reported from each precinct.
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In many [[Condorcet method]]s, each ballot can be represented as a two-dimensional square array referred to as a pairwise matrix. The sum of these matrices may be reported from each precinct.
[[Instant-runoff voting]] does not comply with the summability criterion.
''' See also '''
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[[Category:Voting system criteria]]
== Summability criterion ==
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