Difference between revisions of "Ballot"

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See [[Preferential voting]]. A ranked ballot involves ranking candidates i.e. A>B>C means A is better than B, and B is better than C, with A being implied to be better than C as well. Some ranked ballot implementations allow you to skip rankings i.e. A>skipped ranking>B, and also allow you to rank candidates equally i.e. A>B=C>D=E=F means A is better than everyone else, B and C are equal but better than everyone except A, and D, E, and F are worse than the other ranked candidates, but the voter has no preference between them.
A ranked ballot can be thought of as either imposing [[transitivity]] on voters' preferences in every possible [[runoff]] (based on [[pairwise counting]]), or as asking voters who they would elect if it was up to them, then asking them who'd they elect if that candidate was ineligible to win, etc. Note that a ranked ballot can be reconstructed from a voter's pairwise preferences using a [[Copeland]] ranking (i.e. the candidate(s) whom the voter prefers against the most other candidates are their 1st choices, etc.), but that a rated ballot can't be, indicating that ranked ballots collect less information. Note that ranked ballots generally only look at the relations between ranks, not the absolute numbers i.e. a voter who ranks one candidate 2nd and another 7th, while not ranking anyone else, is treated as ranking those candidates 1st and 2nd respectively.
The fundamental idea of ranking is generally that voters are treated as having maximal preferences between every pair of candidates they indicate a preference between; this explains why practically all ranked methods pass the [[majority criterion]] in the two-candidate case.
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