Reveaing the Majority Winner

Blake Cretney bcretney at
Tue Nov 10 12:53:40 PST 1998

On Fri, 06 Nov 1998 01:58:28   Bart Ingles wrote:
>Blake Cretney wrote: 
>> [...]
>> 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

One fear about Condorcet is that a "surprise" winner could result
who hasn't gone through the kind of media scrutiny that front
runners go through.

48 A B C
5  B
47 C B A

Since the front-runners are A and C, we would imagine they would get
most of the coverage.  When B wins, he may be untested.  At least
that's the theory.  However, the big assumption being made in this
argument is that even though the election is being held by a 
Condorcet method, everyone acts as if it is plurality.

My point is that polls will tell us that B is a "front-runner" in the
sense of being likely to win.  So it doesn't matter that B wouldn't
have been a front-runner under plurality, B will get the scrutiny of
a front-runner.

If A voters still think B is preferable to C, and C voters think B
is preferable to A, I don't see why we should second guess them.

Related to this is the "Unknown is Average" theory.  The idea is
that voters will perceive unknown candidates as central ideologically.
So, in the above example, voters may vote for B over the candidate
of the other extreme just because they don't know anything about
him and therefore assume he is better than a candidate they consider
particularly bad.

Of course, the above argument applies again.  If voters feel this way,
B will become a "front-runner" and whether the support is deserved
will be tested.  However, I think the problem with this argument
goes deeper.  The problem is that voters don't really think that
way.  In fact, if they did, this argument wouldn't have much 
rhetorical value.  People wouldn't understand why electing unknown
candidates was a problem.  They would say, "Oh well, at least
electing an unknown candidate is better than electing a candidate
from the opposite side of the political spectrum from my candidate."

Another simpler reason this is not a problem is laziness.  Voters
won't want to rank all the candidates on their ballot, just to be
able to rank some major candidate last.  Unless the method gives
some sensible strategic reason for them to do so, they won't.  The
exception is "below the line" ballots, which implicitly endorse
this kind of voting.

>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.

By "overall support", what do you mean.  First place votes, or is
there some other standard you have in mind.  I'm not sure that
"overall support" can be defined, but I certainly wouldn't
define it to mean first place votes.

>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

I try to avoid relying on intuition too much to determine a winner.
For example, many people intuitively feel that the candidate who
receives the most first place votes should win.  It's not surprising
when people feel that way, since that's the method we're all used to.
Its the method we have observed used most often, and it is the method
we were taught as children.

Many, if not most, people intuitively feel that there should be some
minimum level of first choice support required by a winner.  Even
among those who partly abandon plurality because of its problems,
there is a desire not to get results that are too different from it.
However, we should ask whether this is a rational requirement or
whether it is just the remnant of the plurality-type thinking that
we were all taught and all believed before we knew that other methods
were possible.



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