Summability criterion: Difference between revisions
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(Did a bit more cleanup based on EM posts, subdividing the full criterion into three conditions.) |
(Added academic article that references non-summability.) |
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Unlike most other voting system criteria, it does not relate to the end result, only to the process. |
Unlike most other voting system criteria, it does not relate to the end result, only to the process. |
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This is important for elections with 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 with 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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==Requirements== |
==Requirements== |
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Informally speaking, the amount of data that has to be transmitted from the precincts should be less than the amount of data on the ballots themselves. In other words, it must be more efficient to count the votes in precincts than to bring the votes to a centralized location. |
Informally speaking, the amount of data that has to be transmitted from the precincts should be less than the amount of data on the ballots themselves. In other words, it must be more efficient to count the votes in precincts than to bring the votes to a centralized location. |
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*Some Condorcet hybrids (e.g. [[Nanson's method]], [[Majority Choice Approval]]) |
*Some Condorcet hybrids (e.g. [[Nanson's method]], [[Majority Choice Approval]]) |
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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> |
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> Potthoff also observes that [[IRV]] is not summable.<ref name="Potthoff 2011 pp. 101–122">{{cite journal | last=Potthoff | first=Richard F. | title=Simple manipulation-resistant voting systems designed to elect Condorcet candidates and suitable for large-scale public elections | journal=Social Choice and Welfare | publisher=Springer Science and Business Media LLC | volume=40 | issue=1 | date=2011-08-31 | issn=0176-1714 | doi=10.1007/s00355-011-0589-3 | pages=101–122}}</ref> |
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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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