[EM] 3 or more choices - Condorcet

[Chris Benham]

Robert Bristow-Johnson wrote (1 Oct 2012):

"my spin is similar.  Ranked Pairs simply says that some "elections" (or 
"runoffs") speak more loudly than others.  those with higher margins are 
more definitive in expressing the will of the electorate than elections 
with small margins.  of course, a margin of zero is a tie and this says 
*nothing* regarding the will of the electorate, since it can go either way.

the reason i like margins over winning votes is that the margin, in vote 
count, is the product of the margin as a percent (that would be a 
measure of the decisiveness of the electorate) times the total number of 
votes (which is a measure of how important the election is).  so the 
margin in votes is the product of salience of the race times how 
decisive the decision is."

Say there are 3 candidates and the voters have the option to fully rank them,
but instead they all just choose to vote FPP-style thus:

 
49: A
48: B
03: C
 
Of course the only possible winner is A. Now say the election is held again (with
the same voters and candidates), and the B voters change to B>C giving:


49: A
48: B>C
03: C


Now to my mind this change adds strength to no candidate other than C, so the winner 
should either stay the same or change to C. Does anyone disagree?
 
So how do you (Robert or whoever the cap fits) justify to the A voters (and any fair-minded 
person not infatuated with the Margins pairwise algorithm) that the new Margins winner is B??
 
The pairwise comparisons: B>C 48-3,  C>A 51-49,  A>B 49-48.

Ranked Pairs(Margins) gives the order B>C>A. 

I am happy with either A or C winning, but a win for C might look odd to people accustomed
to FPP and/or IRV.

 
*If* we insist on a Condorcet method that  uses only information contained in the pairwise
matrix (and so ignoring all positional or "approval" information) then *maybe* "Losing Votes"
is the best way to weigh the pairwise results. (So the strongest pairwise results are those where
the loser has the fewest votes and, put the other way, the weakest results are those where the
loser gets the most votes).

 
In the example Losing Votes elects A. Winning Votes elects C which I'm fine with, but I don't
like Winning Votes for other reasons.

Chris Benham
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