4
Condorcet loser, who would lose in pairwise contests to every other candidate, may turn
out to be the most acceptable candidate.
To justify this last statement, we need to define some measure of “acceptability.”
If voters rank candidates from best to worst, where they draw the line in their rankings
between acceptable and unacceptable candidates offers one such measure. It is precisely
this information that is elicited under approval voting (AV), whereby voters can approve
of as many candidates as they like or consider acceptable. This gives them the
opportunity to be sovereign by expressing their approval for any set of candidates, which
no other voting system permits.
elect and
to prevent the election of candidates, as we will prove.
Call a candidate a Pareto candidate if there is no other candidate that all voters
rank higher. We demonstrate that candidates selected under AV always include at least
one Pareto candidate. In fact, AV dominates so-called scoring systems, including
plurality voting (PV) and the Borda count (BC), with respect to the election of Pareto
candidates: A Pareto candidate elected by a scoring system is always elected by AV for
some sincere and admissible strategies, but not vice versa. This is also true for ranking
systems that do not rely on scoring, including the Hare system of single transferable vote
(STV) and the majoritarian compromise (MC), as we will show.
Center for Applied Economics at New York University.
2
Voter sovereignty should be distinguished from Arrow’s (1963) condition of “citizen sovereignty,”
whereby for any two alternatives a and b, if all voters prefer a to b, a cannot be prohibited as the social
choice. If voters are “sincere,” AV satisfies citizen sovereignty, because all voters who approve of b will
also approve of a. Note that voter sovereignty describes the behavior of individual voters whereas citizen
sovereignty is a property of a voting system.
Convention