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 ==

The following text is derived from text that 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> See the edit history for the old page for more details.<ref>Edit history for "Summability criterion" on English Wikipedia: https://en.wikipedia.org/w/index.php?title=Summability_criterion&action=history</ref>

According to a deleted Wikipedia article<ref name=":0" />, the following methods comply with the summability criterion:

* [[Majority Choice Approval]]

* [[Schulze method]]

The [[summability criterion]] is a [[voting system criterion]], used to objectively compare [[voting system]]s. The criterion states:

* [[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>

<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>

'''Complying methods'''

[[Majority Choice Approval]], [[Schulze method]], [[Approval voting]], [[Range voting]], [[Borda count]], [[Borda count|Nanson's method]], and [[Plurality voting]] all comply. [[Instant-Runoff Voting]] does not comply.

'''Commentary'''

Summability is the only publicly expressed criterion that addresses implementation logistics. Election methods that comply with the summability criterion are easier to implement than those that do not. Those who support the summability criterion say that it is essential for ensuring the integrity of an election.

Under methods that do not comply with the summability criterion, usually every individual vote (rank list) or at least every unique vote and its number of occurrences, must be available at a central location to determine the winner. The votes cannot feasibly be compressed by summing, as in other election methods.

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~~'''~~Summability of various methods~~'''~~

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== 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. ~~<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>~~

[[Instant-runoff voting]] does not comply with the summability criterion.

'''References'''

''' See also '''

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[[Category:Voting system criteria]]

</blockquote>

Note that it 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)]].

== Summability criterion ==