Difference between revisions of "Ballot"

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Two rated ballots that use different scales can be converted to each other. For example, if one voter gave a candidate a 5 out of 10 and another voter gave a candidate a 3 out of 7, the 5 out of 10 can be interpreted as a 3.5 out of 7, and the 3 out of 7 as a 4.2857 out of 10. In general, all rated ballots can be thought of as approximations of (and transformable into) a scale from 0 to 1 (or 0% to 100%), with 0 being no support and 1 being full support.
 
The general idea of rating is that a voter's [[Pairwise counting|pairwise]] preferences are connected i.e. if a voter indicates A is maximally better than B (by giving A the max score and B the min score), then they must indicate B is no better than C.
 
=== Ranked ballot ===
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.
 
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.
 
== Write-in option ==
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