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Voter Sovereignty and Election Outcomes
1. Introduction
Our thesis in this paper is that several outcomes of single-winner elections may be
acceptable. Perhaps the most dramatic recent example illustrating this proposition is the
2000 US presidential election, in which George W. Bush won the electoral vote—
disputed though it was in Florida—and Al Gore won the popular vote. Each of these
candidates could claim to be the winner according to one of these criteria, but only the
electoral vote mattered in the end.
To be sure, the extreme closeness of this election was unusual. But many
elections, especially those with three or more candidates, may have more than one
acceptable outcome.
For example, even when there is a Condorcet winner, who can defeat every other
candidate in pairwise contests, there may be a different Borda-count winner, who on the
average is ranked higher than a Condorcet winner. If there is no Condorcet winner
because of cyclical majorities, the Condorcet cycle may be broken at its weakest link to
select the strongest candidate in the cycle, who need not be the Borda winner.
That different voting systems can give different outcomes is, of course, an old
story. The observation that different outcomes may satisfy different social-choice criteria
is also old hat (Nurmi, 1999, 2002, and Brams and Fishburn, 2002, give many examples).
What is new here is our claim that in an election with three or more candidates, other
outcomes—not just the Condorcet winner, the Borda-count winner, or the strongest
candidate in a cycle—may be more acceptable to the electorate. In fact, even a
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We thank Eyal Baharad, Dan S. Felsenthal, Peter C. Fishburn, Shmuel Nitzan, Richard F. Potthoff, and
Ismail Saglam for valuable suggestions. Steven J. Brams acknowledges the support of the C.V. Starr
Convention