Re: Why plurality is not "wrong"

From: Jeff Almeida <spud_at_spudzeppelin_dot_com>
Date: Fri Apr 16 2004 - 23:45:54 CDT

Also Sprach David Mertz:
>Jeff has been pushing the notion that plurality voting is somehow wrong
>technically, not simply something he disagrees with politically.

>Jeff's notion is simply misguided--Jeff's criteria for what he would
>consider the "correct" outcome is not uniformly shared by all voters
>(or probably even most voters).

Nonsense. You're making the assumption that I care (in a mathematical
sense; obviously I do have a political opinion on the subject) which of
the other outcomes is chosen -- I do not. The problem with plurality is
not the sort of Al-George-Ralph problem people generally use where two
candidates are close and which one wins is determined (or not) by the
failed second-choice of the minor candidate. The problem with plurality
is the degenerate case that lives at the very center of the solution
space, the one Saari talks about WRT both Jesse Ventura and his famous
"Band Vacation to Upper Michigan" text.

Fundamentally, while it is reasonably difficult (in fact, Arrow's theorem
suggests a scenario could exist where the choice of counting method could
make any one of the three win) to determine the winner of such a three-way
contest, it is on the other hand fairly simple to determine who should NOT
win such a race: if you admit ANY non-cyclic order relation on the
candidate set for each voter, then should any one of the candidates be the
last place choice of a majority of the electorate, it is reasonable to
conclude that that candidate should not win the election. Unfortunately,
that is precisely what happened in Minnesota in 1998, where poll numbers
suggest overwhelming percentages of Coleman voters preferred Humphrey to
Ventura and vice-versa.

To borrow Saari's quote from an article in the November 2000 issue of
Discover magazine, "The plurality vote is the only procedure that will
elect someone who's despised by almost two thirds of the voters." THAT is
the fundamental flaw with pluralities, and it is a technical, not a
political problem. For further contrast of pluralities v. runoffs, I'd
point you to sec. 3.5.5 of Saari's book "Geometry of Voting"
(Springer-Verlag, 1994).

Besides which, if you read what I have been saying closely, I have never
argued that we should be unwilling to tabluate a plurality winner. All
I'm asking is that we include a blanket caveat that pluralities are more
likely to admit aborrent results, much like using a toaster while sitting
in a bathtub.

jeff :)

Jeff D. "Spud (Zeppelin)" Almeida
Corinth, TX
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Received on Fri Apr 30 23:17:09 2004

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