Difference between revisions of "Consistency criterion"

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Add reference to Young, improve description.
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(Add reference to Young, improve description.)
The '''consistency criterion''' requires that any candidate who wins both of two separate sets of voters must also win the combined electorate. AlthoughIn itthis isdefinition, not"winning" aalso logicalincludes requirement,being generallytied speakingfor systemsfirst whichplace: satisfyif thea consistencycandidate criterionX alsoties with some other candidate satisfyin the [[participationfirst criterion]].electorate, Theand reversewins implicationoutright isin alsothe commonsecond, thoughX slightlymust win outright in the lesscombined soelectorate.
Although it is not a logical requirement, generally speaking systems which satisfy the consistency criterion also satisfy the [[participation criterion]]. The reverse implication is also common, though slightly less so.
A [[voting system]] is '''consistent''' if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. If a voting system is not consistent then it may be manipulated through the establishment of strategically configured election districts.
==Complying Methodsmethods==
A strict [[preferential voting]] method is "consistent if and only if it is a scoring function"<ref name="Young 1975 pp. 824–838">{{cite journal | last=Young | first=H. P. | title=Social Choice Scoring Functions | journal=SIAM Journal on Applied Mathematics | publisher=Society for Industrial & Applied Mathematics (SIAM) | volume=28 | issue=4 | year=1975 | issn=0036-1399 | doi=10.1137/0128067 | pages=824–838 |url=http://www.eecs.harvard.edu/cs286r/courses/fall11/papers/Young75.pdf}}</ref>, i.e. a [[weighted positional method]] or a combination of these where one or more weighted positional methods are used in sequence to break the ties of another. If the preferential voting method admits weak preference orders (rankings with equal-rank or truncation), it must reduce to a scoring function when no voters make use of equal-rank or truncation.
<!-- It would be nice to find a reference that handles weak preference orderings, but I haven't been able to find one. -->
[[Plurality voting]], [[Approvaland voting]], [[Cardinal Ratings]],the [[Borda count]], andare Woodall'sweighted [[Descendingpositional Acquiescing Coalitions|DAC]]methods and [[Descending Solid Coalitions|DSC]] methods allthus pass the Participationconsistency Criterioncriterion. [[Condorcet method | Condorcet methods]], [[Majority Choice Approval]], and [[IRV]] fail.
In addition, [[Approval voting]] and [[Score voting]] are consistent. If X is the winner in the first district, then that means that X's score is greater than or equal to any other Y, and the same for the second district. Then summing the districts' scores can not make any Y's sum exceed X's sum.
[[Plurality voting]], [[Approval voting]], [[Cardinal Ratings]], [[Borda count]], and Woodall's [[Descending Acquiescing Coalitions|DAC]] and [[Descending Solid Coalitions|DSC]] methods all pass the Participation Criterion. [[Condorcet method | Condorcet methods]], [[Majority Choice Approval]], and [[IRV]] fail.
[[Category:Voting system criteria]]
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