Revealing the Majority Winner

Bart Ingles bartman at
Tue Nov 10 17:32:18 PST 1998

Blake Cretney wrote:
> [...]
> 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.
> [...]
> 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.

This goes along with one of my points, advocating tiebreakers that don't
discourage truncation.

> >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.

By "overall support" I mean most strongly the number of first choice
votes, less strongly lower votes.  I suppose this implies either some
sort of weighting mechanism, or else a method where the top votes are
more likely to be used than the lower votes.  I have no definite formula
for this, I guess "desirability * votes" or "utility * winnability" are
as good as any.

I realize that the rankings are relative, and not measures of absolute
desirability.  Because of this I think the more conservative approach is
to assume fairly low levels of desirability for the intermediate ranks. 
The only ranks we really know about are the first and last, and I'm not
so sure about the last.

AV/IRO attempts to use the weakest first choice as a proxy for lowest
"overall support" or "absolute desireability".  It may not be the ideal
substitute, but at least it's a reasonable one.  Intermediate choices
are used at full value, but the probability of use declines with rank. 
Sequentially dropping the weakest candidate probably helps reduce the
chances of electing the "wrong" candidate (some Condorcet tie breakers
presumably drop weakest defeats for the same reason).

If the first choice doesn't mean more than lower choices, why do we all
seem to agree that a candidate with 50.1% of the first choice vote
should win over someone with 100% of the second choice vote?


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