# [EM] Top Three Condorcet

Dave Ketchum davek at clarityconnect.com
Wed Jun 9 13:01:12 PDT 2004

```On Wed, 9 Jun 2004 09:56:24 -0700 (PDT) Forest Simmons wrote:

> 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
>>>
>>>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
>>>
>>>
>>
>
> 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.
>

I am not ready to try to name this creature, which I doubt deserves existence.

Neither do I claim the muscle to be able to demand renaming, unless
someone else sees what I see and joins in.

What I see as Condorcet is that it is an IMPORTANT method name, and that
its voting is on a ranked ballot, with NO COMPLICATIONS for the voter such

I also see it usable in an election for governor, with the arrays of vote
counts being the ONLY information forwarded by precincts for central
summing and analysis.

>
>
>>Finally:
>>      If there is no cycle, what is there to brag about here?
>>
>
> Depends on the way that the three finalists are chosen.
>

Again, if there is no cycle in the voters' ranking, what value would there

>
>>      If there is a three way cycle, why not solve it via Condorcet?
>>
>
> That's exactly what is proposed here.
>

In context, my saying "in voters' ranking" should clarify.

>
>>      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.
>

Same as above - point is that Condorcet has no trouble disposing of all
the minor candidates that are not in a cycle.  Here I claim that it should
be rare, indeed, to have more than three candidates strong enough to be in

> Forest

--
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Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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```