Difference between revisions of "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 voting|choose-one]] a.k.a. [[Single-mark ballot|single-mark ballots]] (you mark one candidate that you support out of all candidates; these are often considered as "[[Bloc voting|choose up to as many candidates as there are seats to be elected]]" a.k.a bloc voting ballots because when there are, say, two winners to be chosen, usually voters are allowed to mark up to two candidates, etc. [[Cumulative voting]] ballots can be considered a variation.), [[Approval ballot|Approval ballots]] (mark all the candidates that you support), [[Ranked ballot|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 [[Ratings ballot|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|approval threshold]] is utilized, and in fact, an [[Approval voting#Ballot types|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. A ranked ballot can be (at least partially) reconstructed from any of the other three ballot types i.e. if a voter scored one candidate higher than another (or marked one candidate but not another), then it is known for certain that that voter would also rank that candidate higher than the other.
{| class="wikitable"
|+Relation table
| ---
(Is equivalent to an approval, or cumulative, ballot when unlimited numbers of candidates can be marked).
(Is equivalent to a choose-one ballot when only one candidate can be approved).
| ---
(Is equivalent to a rated ballot when only two ratings are allowed.)
|Yes (one of the candidates ranked 1st would be marked on a choose-one ballot)
|Only if an approval threshold is used (or if the voter ranked every candidate either 1st or last; it must also be assumed the voter would approve anyone they ranked 1st).
| ---
|Only if the voter ranked every candidate 1st or last.
|Yes (one of the candidates scored highest by the voter would be marked on a choose-one ballot)
|Only if an approval threshold is used (or if the voter rated every candidate either at the highest or lowest score).
(Is equivalent to an approval ballot when only two ratings are allowed.)
|Yes (though with a slight caveat: only to the extent that enough scores were allowed i.e. if there are 7 candidates, and the voter has a preference between each of them, but was only allowed to give each of them one of 6 scores, then by pigeonhole principle they would've had to lie and indicate an equal preference between at least 2 of them, so the reconstructed ranking won't be perfectly accurate).
| ---
(The intersection between ballot types indicates relations. For example, the cell in the third row and fourth column indicates whether approval ballots give the information required to reconstruct a ranked ballot and with how much reliability).
This table shows that generally speaking, a rated ballot without an approval threshold provides the most information of any ballot type without an approval threshold, and that a rated ballot with an approval threshold provides the most information of any ballot type.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:<blockquote>Alicia[X] Brandon[] Charlie[] David[] Eileen[X]</blockquote>meaning "Alicia and Eileen are supported by this voter"<blockquote>or Alicia>Eileen=(approval threshold)>Brandon=Charlie=David</blockquote>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"
It's important to keep in mind that voters may be incentivized to show or not show weak preferences between candidates based on ballot type. For example, a voter who thinks candidate A is a 10/10 and candidate B is a 9/10 may rank the two candidates equally or approve both of them on ranked or Approval ballots, respectively, in order to avoid exaggerating their preference between the two. So sometimes converting between one ballot type to another involves losing some of this information.
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.
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