Summability criterion: Difference between revisions

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(Okay, I think I'll declare this "merged". There's a lot more copyediting that needs to happen, but I've been working on this long enough.)
(→‎Compliance: More copyediting)
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This is important for elections wtih many voting jurisdictions to be able to practically transmit their vote totals for tabulation. Summability is important to be able to report real-time combined vote totals in an understandable way. Some non-summable methods require that the individual ballot images are are transmitted to a centralized counting location to find the combined result.
This is important for elections wtih many voting jurisdictions to be able to practically transmit their vote totals for tabulation. Summability is important to be able to report real-time combined vote totals in an understandable way. Some non-summable methods require that the individual ballot images are are transmitted to a centralized counting location to find the combined result.
== Compliance ==
== Compliance ==
Back in 2009, [[English Wikipedia]] stated that the criterion was stated as follows:<ref>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></ref><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><ref>Note that this blockquote was copied to [[electowiki]] before it was deleted. There were other changes may have been made after the article was copied to [[Summability criterion (Wikipedia version)]].</ref></blockquote>According to a deleted Wikipedia article<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>, the following methods comply with the summability criterion:
Back in 2009, [[English Wikipedia]] stated that the criterion was stated as follows:<ref>An article titled "[[wikipedia:Summability criterion|Summability criterion]]" was deleted from [[English Wikipedia]] in 2009.<nowiki><ref></nowiki>[[English Wikipedia]] AfD for "Summability Criterion": https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Summability_criterion



*[[Majority Choice Approval]]
Before the page was deleted from Wikipedia, it was copied to [[Electowiki]]. Those with the correct permissions can see the edit history on English Wikipedia.</ref> <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><ref>Note that this blockquote was copied to [[electowiki]] before it was deleted from [[English Wikipedia]]. There were other changes may have been made after the article was copied from [[wikipedia:Summability criterion]] to [[Summability criterion (Wikipedia version)]]. Please see the edit histories for each page to determine who authored the passage you are interested in.</ref></blockquote>Here at [[electowiki]], we believe the following methods comply with the summability criterion:
*[[Schulze method]]

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*[[Plurality voting]] (also known as "choose-one voting") — In [[plurality voting]], the number of ballots for each candidate may be counted, and these totals reported from each precinct.
*[[Approval voting]] — Though each ballot may contain votes for more than one candidate, the sum of all values for each candidate may be found at each precinct and reported.
*[[Approval voting]] — Though each ballot may contain votes for more than one candidate, the sum of all values for each candidate may be found at each precinct and reported.
*[[Borda count]] — Though each ballot contains votes for more than one candidate, and these votes may have different values, the sum of all values for each candidate may be found at each precinct and reported.
*[[Borda count]] — Though each ballot contains votes for more than one candidate, and these votes may have different values, the sum of all values for each candidate may be found at each precinct and reported.
* [[Range voting]] — Though each ballot contains votes for more than one candidate, and these votes may have different values, the sum of all values for each candidate may be found at each precinct and reported.
* [[Score voting]] — Though each ballot contains votes for more than one candidate, and these votes may have different values, the sum of all values for each candidate may be found at each precinct and reported.
* Most [[Condorcet method|Condorcet methods]] (e.g. [[Schulze method]], [[Ranked Pairs]]) — these can generally be added into a two-dimensional array
*[[Borda count|Nanson's method]]
* Some Condorcet hybrids (e.g. [[Nanson's method]], [[Majority Choice Approval]])
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*[[Plurality voting]] — In [[plurality voting]], the number of ballots for each candidate may be counted, and these totals reported from each precinct.


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>
As noted in 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>


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.
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.
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