The Problem of Strategic Behavior under Approval Voting

Abstract

Approval voting is being promoted as “the election reform of the 20th century” (Brams, 1980, p. 105), and indeed if voters' preferences are dichotomous, approval voting has some remarkable qualities: it is uniquely strategy-proof, a candidate wins if and only if he is a Condorcet winner, and voters have simple strategies that are at once sincere and sophisticated. However, all of these results depend on the existence of dichotomous preferences, a contrived and empirically unlikely assumption. Here I show that these virtues of approval voting are replaced by some rather undesirable features under more plausible assumptions. More fundamentally, rather than promoting “honest” behavior, as is sometimes implied, the existence of multiple sincere strategies almost begs voters to behave strategically. I also examine sophisticated approval voting and show that in the general case it need not pick a Condorcet alternative. Ironically, there is a condition under which Condorcet winners may always be picked, but for this to occur, voters sometimes have to vote for candidates of whom they disapprove.