The Merits of Approval Voting
MAY 13, 2016
To the Editor:
“Unusual Flavor of G.O.P. Race Illustrates a Paradox” (The Upshot, May
10) gives an incomplete picture of social choice theory.
Yes, the French mathematician the Marquis Condorcet showed that
choices may cycle, and Kenneth Arrow’s generalization of this paradox
showed that there is no perfect voting system, but both results are
founded on the assumption that voters rank candidates. If, instead,
voters grade candidates, these results no longer hold.
The simplest grading system is approval voting, whereby voters
indicate all candidates they find acceptable (give a grade of 1); the
others are deemed unacceptable and receive grades of 0. The candidate
with the greatest number of approvals wins the election.
Under approval voting, there can be no cycle: The candidate who wins
is more approved than every other candidate in paired comparisons.
Because approval voting does not restrict voters to supporting only
one candidate, it tends to elect the most acceptable candidate over
all, not the strongest minority candidate who benefits from a divided
field.
In the 2016 Republican primaries, polls show that Donald Trump was not
acceptable to a significant portion of Republican voters, so he would
not have done nearly as well under approval voting.
STEVEN J. BRAMS
New York
The writer is a professor of politics at New York University and the
author of “Mathematics and Democracy: Designing Better Voting and
Fair-Division Procedures.”
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Warren D. Smith
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