[EM] 05/13/02 - The Education of Poor Richard:

[Michael Rouse]

----- Original Message -----
From: "Donald Davison" <donald at mich.com>
To: "[EM]" <election-methods-list at eskimo.com>
Sent: Monday, May 13, 2002 5:35 AM
Subject: [EM] 05/13/02 - The Education of Poor Richard:

> Whenever anyone uses the code words `Condorcet Winner' they are attempting
> to establish Condorcet to this high position as the standard of all
> single-seat election methods including Condorcet itself.  I do not accept
> Condorcet as the standard, but of more importance I say it is dishonest to
> regard any method to be a standard of all methods including itself.  This
> dishonesty will create junk mathematics and I said as much in my reply to
> Alex's use of the code words.

I have to agree with Forest Simmons -- saying  that the "Condorcet Winner"
is one criterion in evaluating elections is not the same as saying it is the
*only* criterion. There are other important criteria that should be
considered: the Majority Criterion, the Monotonicity Criterion, and the
Independence of Irrelevant Alternatives Criterion, to name a few.

Nor is it saying that the Condorcet method should be the single unassailable
"gold standard" by which all other methods are measured, only that it has a
"common sense" property (that if one candidate can beat any other in a
one-on-one race, then that candidate should be the winner) that is useful in
comparing other voting methods. You can, if you prefer, replace each
occurrence of "Condorcet Winner" with "the winner of all head-to-head
matchups" or "pairwise winner."

In its favor, Instant Runoff Voting does pass the Majority Criterion. So
does Condorcet. One strike against Condorcet voting is that it fails the
Independence of Irrelevant Alternatives Criterion -- although only when
there is a circular tie, where the "irrelevant alternative" is part of the
cycle. Unfortunately, IRV violates IIAC as well, *and* it violates
monotonicity. If the possibility that your second-place vote could help
defeat your primary candidate is a problem, how much worse is the
possibility that greater preference for a candidate can defeat him? (Others
have posted examples of this, and they are "contrived" only in the sense
that all hypothetical examples are contrived.)

For me, the biggest argument against IRV is the "Exclusion of the Compromise
Candidate." Given uniform distribution, if less than two-thirds of the
electorate lies between two candidates of equal strength and opposite
political viewpoint, it is impossible for a third "central" candidate to
win. With three candidates, the winner will be the fringe (right-wing or
left-wing) candidate that takes enough votes from the central candidate to
win instead of the candidate that best represents the views of the
electorate as a whole.

It's easy to illustrate this graphically: Draw a line segment with marks
one-sixth the distance from the left end, in the center, and one-sixth the
distance from the right end. Given uniform voter distribution, as long as
the left-wing candidate is between his mark and the center and the
right-wing candidate is between his mark and the center, the center
candidate will always lose with IRV (i.e. have fewer voters closer to it
than to another candidate) *no matter where it is placed between the two
extremes*. One extreme or the other will always win. Of course, actual voter
distributions are more bell-curve than linear, but that just changes where
you draw the end marks, not the exclusion of the compromise candidate.

Michael Rouse
mrouse at cdsnet.net

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