Independence of Irrelevant Ballots: Difference between revisions

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Revision as of 18:44, 10 November 2023 (view source) Toby (talk \| contribs) (Added category) ← Older edit		Revision as of 17:17, 11 December 2023 (view source) Toby (talk \| contribs) (Blank Ballot link redirects to same article. Integrated Blank Ballots into the article better. Further information added.) Newer edit →
Line 1: Independence of Irrelevant Ballots (IIB), isalso ~~equivalent~~known toas the [[Blank Ballot Criterion~~]]. It~~, says that a voter who has no preference between any candidates should not impact which of them wins or loses by voting. A ''blank ballot'' or ''irrelevant ballot'' is a ballot that fails to indicate any preference between any of the candidates. For ranked-ballot methods, this would mean all candidates are equally ranked or left unranked. For score or graded methods, this would mean that each candidate is given the same bottom-level or positive score/grade. For approval voting, every candidate would be approved or every candidate unapproved. A generalization of this concept is to treat an irrelevant ballot as simply being a ballot with no preference between the candidates in a set of candidates, and the requirement as being that that ballot shouldn't impact who wins or loses among that set of candidates. In general, [[Largest remainder method\|Largest remainder methods]] violate this criterion because an irrelevant voter will change the size of the quota. See the [[Quota rule#Notes]] for an example. There are proportional cardinal methods that pass this criterion with "empty ballots" (where all candidates are given a zero or unapproved) but fail with "full ballots" (where candidates are given the same positive score or approved). For example, [[Phragmen's voting rules]] passes with empty ballots but fails with full ballots. [[Monroe's method]] fails with both full and empty ballots. In general, it is easier for a method to pass this criterion with empty ballots. ~~== Blank Ballot Criterion ==~~ ~~=== Definitions ===~~ A ''blank ballot'' is a ballot that fails to indicate any preference between any of the candidates. For cardinal methods, this can mean each candidate is given a score of zero or the same positive score (including approval in approval methods). ~~=== Statement of Criterion ===~~ ~~The addition of one or more blank ballots cannot change the winner.~~ === Complying Methods === * '''Complies''': [[Approval voting]], [[Cardinal Ratings]], [[Schulze method\|Schulze]], [[COWPEA]], [[COWPEA\|COWPEA Lottery]], [[Proportional_approval_voting\|Propotional Approval Voting]] * '''Fails''': [[Median Ratings]], [[Phragmen's voting rules]], [[Monroe's method]] [[Category:Voting system criteria]]