[EM] Top Three Condorcet

[Dave Ketchum]

HELP:  Need some input for the Jargon Dictionary - Who is right, Forest or
myself?

Forest is proposing a "class of methods" (see below) in which the ballots
include both rankings, as we expect for Condorcet, AND ratings or grades,
as are used in some other methods.

  I do not object to his offering a class of methods - that is expected in 
EM and, occasionally, something good comes of it, BUT:
      Forest uses "Condorcet" in the group name.
      I claim that word should be reserved for methods using the ranked 
ballots I (and others) expect for Condorcet methods.

Dave Ketchum

On Thu, 10 Jun 2004 13:18:01 -0700 (PDT) Forest Simmons wrote:

 > On Wed, 9 Jun 2004, Dave Ketchum wrote:
 >
 > [...]
 >
 >
 >>All of this because I objected to Forest using "Condorcet" in a
 >>method name when the method involved ratings (he uses the word
 >>"grade" which seems to me to be a synonym for rating).
 >>
 >
 > Well, let that be a lesson to you :|]
 >
 > To clear up the misunderstanding, "Top Three Condorcet" is not a method
 > name, but is the name of a class of methods that have in common one thing:
 > they use Condorcet's method to choose the winner from among three
 > finalists.  At that stage (if not before) only the relative rankings (with
 > equality allowed) of the three finalists is used as input to Condorcet.
 >
 >>From these rankings the pairwise matrix is determined.  It makes no
 > difference if this matrix is processed according to the rules of MAM,
 > CSSD, or MinMax; the outcome will be the same: if there is a cycle, then
 > it will be broken at the weakest link.  Otherwise the finalist that beats
 > both of the others wins.
 >
 > Who has the best idea on how to narrow down to three finalists?
 >
 > Here are some that have already been proposed:
 >
 > 1.  Take the top three approval scorers.
 >
 > 2.  Take the IRV winner along with the last two that IRV would have
 > eliminated.
 >
 > 3.  Take the Buckley winner, the Nanson winner, and the Coombs winner.
 >
 > 4.  Take the MinMax winner along with the two MinMax runnerups.
 >
 > 5.  List the candidates in order of approval. Then (from strongest
 > discrepancy to weakest discrepancy) transpose adjacent candidates in the
 > list until there is no order discrepancy among adjacent pairs. Take the
 > top three candidates from this list.
 >
 >
 > This last suggestion has the advantage of always choosing from the Smith
 > Set, without ever having to explicitly enumerate that set.  Indeed, after
 > the adjacent discrepancies have been removed, the Smith Set will
 > automatically head the list, as surely as the cream rises to the top in
 > Brown Cow yogurt.
 >
 > The discrepancy removal process is just the familiar process of
 > sorting by height a motley line of recruits before undertaking military
 > drill:
 >
 > WHILE any recruit is taller than the one to his/her immediate right,
 >
 > DO switch the adjacent recruits with the greatest such height discrepancy.
 >
 > END
 >
 > This version of Top Three Condorcet is summable, since it only requires
 > the pairwise matrix and the approval scores (which for convenience can be
 > incorporated as diagonal entries in the pairwise matrix).
 >
 > [For ranking purists (who don't like approval cutoffs) substitute Borda
 > Scores for Approval Scores in Method 5.]
 >
 > Any other ideas for Top Three Condorcet?
-- 
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   Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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