Ballot

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A ballot is a voter's expression of preference among the candidates. There are four main ways to do this in the context of voting methods: choose-one ballots (you mark one candidate that you support out of all candidates; these are often considered as "choose up to as many candidates as there are seats to be elected" ballots because when there are, say, two winners to be chosen, usually voters are allowed to mark up to two candidates, etc.), Approval ballots (mark all the candidates that you support), ranked ballots (rank the candidates in order of preference: 1st, 2nd, 3rd, etc. Some ranked ballots allow a voter to give multiple candidates the same rank to indicate no preference between those candidates.) and rated ballots (you rate the candidates on a scale, generally starting from 0, going up to any value, often 5 or 10. Usually only certain in-between values are allowed i.e. if the scale is from 0 to 10, it usually isn't allowed for someone to give a rating of, say, 9.35).

There are several intersections between the various ballot types. For example, the information contained on an Approval ballot can also be found from a ranked or rated ballot if an approval threshold is utilized, and in fact, an Approval ballot is itself a type of rated ballot where the only allowed ratings are "disapprove" and "approve" (0 and 1). A choose-one ballot is itself an Approval ballot with the restriction of only marking one candidate, and can also be thought of as a ranked or rated ballot where only the candidate(s) ranked 1st/rated highest are treated as supported.

As an example of all four ballot types, suppose there are five candidates to consider: Alicia, Brandon, Charlie, David, and Eileen.

Choose-one and Approval ballots are often shown as some form of:
Alicia[X] Brandon[] Charlie[] David[] Eileen[X]
meaning "Alicia and Eileen are supported by this voter"
or Alicia>Eileen=(approval threshold)>Brandon=Charlie=David
meaning "Alicia is my 1st choice, Eileen is my 2nd choice, I approve everyone who is my 2rd choice or higher, and all the other candidates are worse than my 2nd choice" Ranked ballots are often shown as:
Alicia>Eileen>Brandon=Charlie=David
meaning "Alicia is better than Eileen, Eileen is better than any of (Brandon, Charlie, David) and Alicia is also better than any of (Brandon, Charlie, David)". Rated ballots are often shown as:
Alicia:5 Eileen:4 Brandon:3 Charlie:3 David:3
meaning "I give Alicia a score of 5/I give Alicia 5 points, Eileen 4, Brandon 3, etc."

Note that with rated ballots, one might mention what the scale is by putting, for example, Alicia:5/5 (meaning Alicia is a 5 out of 5).

Notes

A common assumption with all four ballot types is that anyone who is not given an explicit marking by the voter is considered worse by that voter than any of their marked candidates, and that the voter has no preference between any of the unmarked candidates.

Pairwise counting can be done on all four ballot types, though ranked and rated ballots offer the most information for this purpose.