Summability criterion: Difference between revisions
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(Continuing to merge (using VisualEditor now). I've created a #Compliance section, and split the voting methods out into bullet points. I've also consolidated the #References sections) |
(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.) |
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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>}} |
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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. |
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== Compliance == |
== Compliance == |
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⚫ | 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: |
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According to a deleted Wikipedia article<ref name=":0" />, the following methods comply with the summability criterion: |
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*[[Majority Choice Approval]] |
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*[[Schulze method]] |
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* [[Approval voting]] |
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*[[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. |
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* [[Range voting]] |
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* [[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. |
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* [[Borda count]] |
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*[[Borda count|Nanson's method]] |
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* [[Plurality voting]] |
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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> |
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> |
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== Summability of various methods == |
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With [[Bucklin voting]], the precinct totals for each candidate at each rank may be summed and reported. |
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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. |
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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[[Instant-runoff voting]] does not comply with the summability criterion. |
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''' See also ''' |
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*[[Voting system]] |
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*[[Monotonicity criterion]] |
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*[[Condorcet Criterion]] |
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*[[Generalized Condorcet criterion]] |
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*[[Favorite betrayal criterion]] |
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*[[Participation criterion]] |
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[[Category:Voting system criteria]] |
[[Category:Voting system criteria]] |
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== Summability criterion == |
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⚫ | The '''summability criterion''' is a criterion about the vote-counting process of |
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'''Vote-counting''' refers to the process of collecting enough information from voters' [[ballot]]<nowiki/>s to find the result of a [[voting method]], as well as how the information is transmitted and processed. |
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== Requirements == |
== Requirements == |