Letter To Scientific American
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Concerning "The Fairest Vote of All"
by Dasgupta & Maskin (March 2004).
A simpler and better voting system is "range voting" where each voter
provides as his vote, a score for every candidate on a 0-10 scale.
The candidate with the highest summed score wins.
My 2000 paper "Range voting" (available as #56 at
www.math.temple.edu/~wds/homepage/works.html; see also #59)
studies it heavily and compares it with numerous other proposed
voting systems by means of millions of computerized simulated
elections. That study clearly showed the superiority of range
voting over all other yet-proposed systems, as measured by a
yardstick called "Bayesian regret".
Dasgupta & Maskin do not actually specify the voting system they are
pushing (!), but I believe that they meant "Black's system," which
dates to the 1950s or earlier. It was described in my paper and
included in my computerized study.
Dasgupta & Maskin completely ignored the massive effects of voters
who vote "strategically" instead of honestly in an attempt to "game
the system." For example, in the 2000 election, many voters who
liked Nader best, instead chose to dishonestly vote (as they
were urged in hundreds of editorials) for Gore, for strategic
reasons ("don't waste your vote"). My paper's theorem 8 shows
that with strategic voters, the winner in an N-candidate
Black-Dasgupta-Maskin election will be exactly the same as the winner
in a plain-plurality election! This theorem destroys Dasgupta & Maskin's
claim that Black's system is superior to plain plurality.
This theorem also holds for the "IRV system" (which Dasgupta &
Maskin also mention but do not describe, but which also is described
and studied in my paper). This is an equally severe indictment of IRV.
My computerized studies allowed either honest or strategic voters,
and allowed adjustable "voter ignorance," and included many different
"utility generators" for creating different election scenarios.
In all, 432 different kinds of scenarios were investigated, running
millions of elections for each. Range voting performed as well
or better than every competing system in every scenario - very
conclusive!
Not only are IRV and Black inferior to range voting on performance
grounds, they also are harder to describe and use and are
more susceptible to near-ties such as Bush-Gore 2000 (since ties
can occur at more than one stage in those procedures).
Dasgupta & Maskin also disserve us by propagating the myth that
the "true majority winner" (if one exists) is the best.
Counterexample: Suppose candidate Hitler, if elected,
will award 51% of the voters 1 dollar worth of societal benefit
but kill the other 49%. Meanwhile candidate Gandhi will award 49%
of the voters 1000 dollars and kill nobody. Everybody knows this
and everybody acts for their own benefit solely.
While Hitler will be the "true majority winner," Gandhi is better
for society as a whole. Range voting with honest voters
would allow the election of Gandhi in this situation, but no
other competing system would.
In conclusion, I point out that the "Bayesian regret"
yardstick is a QUANTITATIVE way to compare voting systems. It
allows estimating the damage society suffers from poor voting system
performance to be translated into extremely real terms such as dollars.
So here are 3 systems:
(1) choose the winner at random (essentially
like monarchy, but probably worse).
(2) Use plurality voting (essentially what happens in most
contemporary democracies).
(3) Use range voting.
My study shows that the societal benefit obtainable by switching
from (2) to (3) EXCEEDS that obtained from switching from (1) to (2),
regardless of whether the voters are honest or strategic. The damage
society is suffering by employing the flawed plurality voting system
thus is absolutely immense, outrageous, and inexecusable.
--Warren D. Smith.
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POSTSCRIPT:
Dasgupta and Maskin in their more formal paper
On the Robustness of Majority Rule and Unanimity Rule
http://www.econ.cam.ac.uk/faculty/dasgupta/
rely heavily on a crude model (due to Duncan Black)
of voters as 1-dimensional single-peaked distributions.
In this model (Black proved, and Dasgupta and Maskin re-proved
in more generality) we have the THEOREM that
"preference cycles" are impossible. That theorem's
validity is due to the fact that, if 3 candidates A,B,C
occur in that order along the 1-dimensional line, then
(in Black's model) no voter can regard B as worse than both A and C.
However, this model is unrealistic (and hence cycles
can and will occur in reality) for several reasons:
1. Real voters are stategic. A voter may well decide
to exaggerate the badness of B, dishonestly ranking him "worst",
for strategic reasons ("don't want to waste my vote").
2. Real voters CAN and SHOULD rank B as worse than both A and C.
For example, suppose the most important issue is whether
to invade and conquer an enemy country that is threatening to
kill us all by next week, or to make a peace treaty with them.
Well, I would pretty much prefer my leader to do one or do the
other, but definitely do it fast. I would NOT want my leader
to take the middle course and do neither.
3. Real voters are not 1-dimensional.
For example, consider the Gore-Bush-Nader 2000 election.
Voter #1 cares about honesty and says that, as far as honesty
is concerned, Nader>>Gore>Bush.
Voter #2 cares about experience: number of years in high office.
So he ranks Gore>Bush>>Nader.
Voter #3 cares about lowering his taxes and figures Nader, as a consumer
advocate, will cut taxes more (or raise them less) than Gore, so
he ranks Bush>Nader>Gore.
The net result of these 3 voters is to create a preference cycle.
The net result of this is that the Dasgupta-Maskin paper
has little connection to reality.
Their paper seems to have a pretty nice theorem in it - albeit
one whose precise statement is rather hard to elucidate - but
it is a theorem that lives in a mathematical fantasy world,
not the real world.
END OF POSTSCRIPT.