Approval voting: Difference between revisions

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.

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 not being as much the case with [[Score voting]] or [[STAR voting]], it is not possible to figure out who the CW is from Approval ballots, since only limited [[pairwise counting]] information can be inferred.

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.

The [[Pairwise counting#Negative vote-counting approach]] approach is based on Approval voting.