[EM] Top Three Condorcet

[Forest Simmons]

On Wed, 9 Jun 2004, Dave Ketchum wrote:

> On Tue, 8 Jun 2004 14:06:19 -0700 (PDT) Forest Simmons wrote:
>
> > If I understand correctly, Beat Path, Ranked Pairs, MinMax, and all of the
> > other serious Condorcet methods are in agreement (except for the
> > margins/wv debate) when there are only three candidates: if one of them
> > beats each of the others pairwise, then that candidate is the winner.
> > Otherwise, the cycle is broken at the weakest link.
> >
> > So why not take advantage of this agreement by using some simple but
> > reasonable method to eliminate all but three candidates and then among
> > those three
> >
> >     If there is a cycle
> >        Then break it at the weakest link
> >        Else go with the one who beats the other two.
> >
> >
> > Elimination methods that eliminate all the way down to two candidates
> > offer too much order reversal incentive, but if there is room for three
> > finalists, then that incentive may be negligible.
> >
> > Here's a more specific proposal along these lines:
> >
> > Use grade ballots.  The three finalists are A the candidate with the
> > greatest number of top grades, B the candidate with the highest grade
> > point average, and C the candidate with greatest number of passing grades.
> >
> > If all three of these turn out to be the same candidate, then this
> > candidate wins.
> >
> > If the set {A,B,C} has only two distinct members, then whichever wins
> > pairwise between them is the method winner.
> >
> > If all three are distinct, and one of them beats the other two pairwise,
> > then that one is the winner.
> >
> > If there is a three way cycle, then the cycle is broken at the weakest
> > link.
> >
> > This method is summable, easy to understand, and hard to criticize, though
> > I'm sure the purists will have plenty to say :')
> >
> > The main disadvantages I see are (1) the controversy over margins versus
> > winning votes, and (2) some folks think that it is too hard to grade the
> > candidates.
> >
> > Any other proposals for Top Three Condorcet?
> >
> > Forest
> >
>
> What is a grade ballot?

A ballot on which each candidate may be graded on some scale, e.g. A
through F or (Steph's idea) A through Z.

>
> Anyway, a method using it should not be called Condorcet.
>

Condorcet's method is used to determine the winner from among the three
finalists.  As long as there are at least three grades, a ranking can be
inferred from the grade ballot.  Actually the name isn't Condorcet, it is
"Top Three Condorcet," a name for a class of methods, not aparticular
method.

If you have a more apt name, I'm willing to consider it.


> Finally:
>       If there is no cycle, what is there to brag about here?

Depends on the way that the three finalists are chosen.

>       If there is a three way cycle, why not solve it via Condorcet?

That's exactly what is proposed here.

>       For other cycles, are we not better off dealing with what should be
> rarities by agreeing as to how to solve them via ranked ballots?


There cannot be other cycles when there are only three finalists.

Forest