Reveaing the Majority Winner

Bart Ingles bartman at
Fri Nov 6 01:58:28 PST 1998

Blake Cretney wrote: 
> There is an apparent conflict between my belief that on average
> preferences towards the end of the ballot are less meaningful, and
> my support of a method that counts a preference between two
> candidates independently of where in the ballot the preference is
> expressed.  That is, if a voter ranks A over B at the beginning of
> the ballot, the method does not differentiate this from voting
> A over B at the end of the ballot.
> Let me first state that although I have never participated in an
> election where rankings are allowed, I know I would have trouble
> ranking many of the lowest candidates.  Elections tend to have
> a number of fringe or protest candidates who receive little
> publicity and have little chance of election.  For most voters,
> a preference between these candidates is likely to be arbitrary.
> However, this doesn't matter.  The method I advocate passes
> MIIAC (Modified Independence from Irrelevant Alternative Criterion).
> What this states is that any expressed preference between two
> candidates who are not in the Smith set has no effect.
> Smith Set-  The smallest non-empty set of candidates where every
> candidate in the Smith set beats every candidate outside the Smith
> set.
> Fringe candidates will not be in the Smith set.  This is because
> to be in the Smith set, a fringe candidate would have to actually
> be majority preferred to a main-stream candidate who IS in the
> Smith set.  It is unlikely that all the main-stream candidates
> will be in the Smith set, let alone fringe candidates.
> [...]

I usually think of a fringe candidate as one who is off to one side of
the spectrum.  My concern here is more about a little-known candidate
who positions himself in the center, or a charismatic candidate who
manages to keep from being pinned down so everyone assumes he is in the
center.  When running against two equally-balanced major candidates, he
can be the sole member of the Smith set with minimal support of his own,
if the other voters rank him above what they see as the 'greater

Against three or more equally balanced major candidates, he doesn't even
need any first-choice votes if he can do better than average in the
rankings.  Example:

6  A B C D
4  A C B D
6  C B D A
4  C D B A
6  D B A C
4  D A B C

A:B  14:16
A:C  20:10
A:D  10:20
B:C  16:14
B:D  16:14
C:D  20:10

B > (A,C,D)    (unless I really have this example screwed up)

I'm not saying that this is a likely outcome, but it may not be as
unlikely as one would expect.  Political factions may tend to equalize
over time, as the loser shifts toward the center in order to recapture
votes (examples: Democrats after 1994, Republicans already doing it
after the last election).  The more equal these factions, the less
overall support required to be the Condorcet winner.

There are probably a number of ways to preventing this, short of
avoiding pairwise methods entirely.  Aside from DEMOREP's (YES/NO)
matrix, other things that might work:  tiebreakers that don't discourage
truncation, reduced weighting for lower pairings, etc.

Maybe the Condorcet criterion should be balanced against other
criteria.  Intuitively, I tend to think a very weak Condorcet winner
should be dropped & those votes used as a tiebreaker to find the AV/IRO
winner; on the other hand, I would drop both CW and AV winner in favor
of the Plurality winner (A) in a situation like:

20  A
1   B C ... Z
1   C D ... Z B
1   D E ... Z B C
1   Y Z B C ... W X
1   Z B C ... X Y

even though one of the other candidates would have 25 votes in the final
round (under IRO), vs. the plurality winner's 20.

Bart Ingles

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