Difference between revisions of "Approval voting"

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However, there is potential for what is known as the [[Chicken dilemma|chicken dilemma]], where one majority subfaction withholds support for the other subtraction to help its candidate win rather than the other subfaction's candidate.
 
=== Alternative names ===
Approval voting is also called set voting or unordered voting, because a voter expresses on their ballot the set of candidates that they prefer above all others, but is not allowed to rank (order) the candidates from 1st to 2nd to 3rd to... to last. In other words, it only allows voters to rank all candidates either 1st or last.
 
=== Unlimited number of candidates can be supported ===
See [[Number of supportable candidates in various voting methods]]. One of the major implications of Approval voting in relation to [[choose-one FPTP voting]] is that with Approval, there is no way to tell (solely with the vote totals for each candidate) whether a voter who supported one candidate did or didn't support another. For example, in FPTP (assuming no equal ranking was allowed, a la [[cumulative voting]]), if Obama gets 30 votes and Romney gets 20, then it is guaranteed that none of the 30 voters who supported Obama also supported Romney, and vice versa. But with Approval, it is possible (albeit unlikely in this example) that everyone who voted for Romney also voted for Obama, and that Obama really only has 10 voters who support him but not Romney. This means that proportional forms of Approval voting are not as precinct-summable as the proportional form of FPTP, [[SNTV]], because not only must one know how many voters approved each candidate to calculate the winner(s) in Approval PR methods, but also which candidates each ballot approved. With choose-one ballots, knowledge of the former yields knowledge of the latter.
 
=== Connection to Condorcet methods ===
The [[Pairwise counting#Negative vote-counting approach]] approach is based on Approval voting.
One of the major implications of Approval voting in relation to [[choose-one FPTP voting]] is that with Approval, there is no way to tell (solely with the vote totals for each candidate) whether a voter who supported one candidate did or didn't support another. For example, in FPTP (assuming no equal ranking was allowed, a la [[cumulative voting]]), if Obama gets 30 votes and Romney gets 20, then it is guaranteed that none of the 30 voters who supported Obama also supported Romney, and vice versa. But with Approval, it is possible (albeit unlikely in this example) that everyone who voted for Romney also voted for Obama, and that Obama really only has 10 voters who support him but not Romney. This means that proportional forms of Approval voting are not as precinct-summable as the proportional form of FPTP, [[SNTV]], because not only must one know how many voters approved each candidate to calculate the winner(s) in Approval PR methods, but also which candidates each ballot approved. With choose-one ballots, knowledge of the former yields knowledge of the latter.
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==== Dichotomous preferences ====
The Approval voting winner is also always someone from the [[Smith set]] if voters' preferences truly are dichotomous (i.e. they don't have ranked preferences, but rather, honestly only support or oppose each candidate).
 
==== Equilibrium ====
Fully strategic Approval voting with perfectly informed voters generally elects the [[Condorcet winner]], and more generally, someone from the Smith set; this is because a plurality of voters have an incentive to set their [[Approval threshold|approval thresholds]] between the Smith candidate and the most-viable non-Smith candidate, resulting in at least the same approval-based margin as the Smith candidate has in their [[head-to-head matchup]] against the non-Smith candidate. A common argument for Approval>[[Condorcet methods]] is that when voters are honest, they get a utilitarian outcome, while if they are strategic, they at least get the CW. This notis beingnot as much the case with [[Score voting]] or [[STAR voting]], but it is not possible to figure out who the CW is from Approval ballots, since only limited [[pairwise counting]] information can be inferred.
 
==== Using pairwise counting to find the result ====
 
 
Here is an example of finding the Approval voting result, and its ranking of all candidates, using [[pairwise counting]] and the [[Smith set ranking]]: <blockquote>30 AB
This could also be done by treating each voter's Approval ballot as a ranked ballot where all approved candidates are equally ranked 1st and all other candidates are ranked last. This shows how Approval can be thought of as a Condorcet method where every candidate must be ranked either 1st or last.
 
==== Strategically electing a pairwise-preferred candidate ====
Supposing rational voters (see [[Approval cutoff#Rationality restrictions]] for examples; chiefly, supposing voters who equally prefer two candidates approve both or neither of them), voters can "simulate" a [[head-to-head matchup]] in Approval voting in the sense that if, between two candidates, the voters who prefer the candidate who pairwise wins the matchup move their [[approval threshold]] between the two candidates, then they can guarantee that the candidate who pairwise loses the matchup is not elected (or if there was a pairwise tie between the two candidates, then they can guarantee a tie between the two candidates). This is because all voters who equally prefer the two candidates will not create an approval-based margin between the two candidates, and because there are more voters who prefer the pairwise winner of the matchup over the other candidate, the pairwise winner will guaranteeably have more approvals (specifically, they will have at least as high an approval-based margin as they do in their pairwise margin over the other candidate). Note however that they can '''not''' always make the pairwise winner of the matchup, or a candidate preferred more than or equally to the pairwise winner by any of the voters who prefer the pairwise winner over the pairwise loser, win. This is most easily seen in [[chicken dilemma]]-type situations; see [[Equilibrium#Notes]] for an example. However, this is true when the winner of the pairwise matchup [[majority-beat]]<nowiki/>s all other candidates.
 
The [[Pairwise counting#Negative vote-counting approach]] approach is based on Approval voting.
 
==See also==
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