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Summability criterion: Difference between revisions
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.
(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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The '''summability criterion''' is a criterion about the vote-counting process of
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>▼
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 ==
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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.
* [[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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*[[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>
▲In [[plurality voting]], the number of ballots for each candidate may be counted, and these totals reported from each precinct.
▲In [[Approval voting]], [[Borda count]], and [[Range voting]], each ballot contains votes for more than one candidate, and, with the last two, these votes may have different values. However, the sum of all values for each candidate may be found at each precinct and reported.
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.
[[Category:Voting system criteria]]
▲The '''summability criterion''' is a criterion about the vote-counting process of voting systems, which describes how precinct-summable a voting method is (i.e. whether there is a way for two areas, known as precincts, to transmit their vote totals and add this up to find the combined vote total, and if so, how easy it is, or if all the votes need to be taken to a centralized counting location to find the combined result). Unlike most other voting system criteria, it does not relate to the end result, only to the process.
== Requirements ==
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