Title
Range voting
Author
Warren D. Smith
NECI, 4 Independence Way, Princeton NJ 08540
wds@research.NJ.NEC.COM
Abstract
The ``range voting'' system is as follows. In a $c$-candidate
election, you select a vector of $c$ real numbers, each of absolute
value $\le 1$, as your vote. E.g. you could vote $(+1,-1,+.3,-.9,+1)$
in a 5-candidate election. The vote-vectors are summed to get a
vector $\vec{x}$ and the winner is the $i$ such that $x_i$ is maximum.
Previously the area of voting systems lay under the dark
cloud of ``impossibility theorems''
showing that no voting system can satisfy certain seemingly reasonable sets
of axioms.
But I now prove theorems advancing the thesis that range voting is
uniquely best among all possible ``Compact-set based, One time,
Additive, Fair'' (COAF) voting systems in the limit of a large number of
voters. (``Best'' here roughly means that each voter has both
incentive and opportunity to provide more information about
more candidates in his vote than in any other COAF system; there are
quantities uniquely maximized by range voting.)
I then describe a utility-based Monte Carlo comparison
of 31 different voting systems. The conclusion of this
experimental study is that
range voting has smaller Bayesian regret than
all other systems tried, both for
honest and for strategic voters for any of
6 utility generation methods
and several models of voter knowledge.
Roughly: range voting entails $3$-$10$
times less regret than plurality voting
for honest, and $2.3$-$3.0$ for strategic, voters.
Strategic plurality voting in turn entails $1.5$-$2.5$ times
less regret than simply picking a winner randomly.
All previous such studies were
much smaller and got inconclusive results, probably because
none of them had included range voting.
%"31" is somewhat deceptive since some are variants of each other.
Keywords
Approval voting, Borda count, plurality, uniqueness, social choice,
strategic voting, Monte Carlo study, Condorcet Least Reversal,
Gibbard's dishonesty theorem, Bayesian regret.