Difference between revisions of "Approval voting"

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.
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.
==See also==