[EM] 3 or more choices - Condorcet

[Ted Stern]

Hi Chris,

You discuss Winning Votes vs. Margins below.

What do you think about using the Cardinal-Weighted Pairwise array in
conjunction with the traditional Condorcet array?

In other words, either WV or Margins is used to decide whether there
is a defeat, but the CWP array is used to determine the defeat
strength, in either Ranked Pairs or Schulze.

To recap for those not familiar with the technique (due to James
Green-Armytage in 2004), a ratings ballot is used: give a score of a_i
to candidate i.  Ranks are inferred: candidate i receives one
Condorcet vote over candidate j if a_i > a_j.

Whenever that Condorcet vote is recorded into the standard A_ij array,
you also tally the difference (a_i - a_j) into the corresponding
CWP_ij location.

Ted

On 08 Nov 2012 08:55:24 -0800, Chris Benham wrote:
>
> 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
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info

-- 
 PO Box 3707  MC 0R-JF                           (Google Voice)  206-552-9611
 Seattle, WA  98124-2207                                  (Fax)  425-717-3652
 http://directorysearch.web.boeing.com/bps/details.asp?bemsid=1660261
 ----------- Frango ut patefaciam -- I break so that I may reveal -----------

-- 
araucaria dot araucana at gmail dot com