Summability criterion: Difference between revisions
→Summability levels
(Added subfactorial-space IRV "pseudo-summable" array for clarity (still not polynomial)) |
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*[[Approval voting]]
*Plurality-based [[Party-list proportional representation|Party list PR]]
*[[Majority Judgment]]{{Note|Requires O(k * n) space, where k is the number of possible ratings and n is the number of votes.}}
*[[Single non-transferable vote]]
*Most forms of [[MCA]]
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*most [[Condorcet method]]s
*Borda-elimination ([[Baldwin's method|Baldwin]]<ref>{{Cite journal|last=Hogben|first=G.|date=1913|title=Preferential Voting in Single-member Constituencies, with Special Reference to the Counting of Votes|url=http://rsnz.natlib.govt.nz/volume/rsnz_46/rsnz_46_00_005780.html|journal=Transactions and Proceedings of the Royal Society of New Zealand|series=|volume=46|issue=|pages=304–308|via=}}</ref> and [[Nanson's method|Nanson]]<ref name="sumNanson">{{Cite journal|last=Nanson|first=E. J.|date=1882|title=Methods of election|url=https://archive.org/details/transactionsproc1719roya/page/197|journal=Transactions and Proceedings of the Royal Society of Victoria|volume=19|pages=197–240|via=}}</ref>)
▲* [[Bucklin voting|Bucklin]]
*[[MCA|MCA-IR]], and some forms of [[MCA|MCA-AR]]
*[[STAR voting]]<ref>{{Cite news|title=Compare STAR and IRV - Equal Vote Coalition|url=https://www.equal.vote/star-vs-irv#simplicity|work=Equal Vote Coalition|access-date=2018-11-12}}</ref>
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===Number of data value types versus number of data values===
Summability focuses to a large extent on the number of data value types, not just the amount of data overall that has to be captured. This can make a difference in certain cases; for example, the regular [[pairwise counting]] approach only requires <math>n^2-n</math> data value types to be captured for all ballots, whereas the [[Negative vote-counting approach for pairwise counting]] requires <math>n^2</math> value types. This is because the latter not only records preferences in each pairwise matchup, but also the number of ballots ranking each candidate. Yet, depending on implementation, the negative counting approach actually has the same upper bound on number of data values to capture as the regular approach, and in practice could require fewer.
===Counting first choices===
Some voting methods can be counted like [[Approval voting]] when counting:
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