[EM] "scored condorcet", etc

[Rob Brown]

Gervase Lam <gervase.lam <at> group.force9.co.uk> writes:
> I don't know what you mean by normalisation here, but it usually means
> some scaling up or down (i.e. multiplication or division).  What I would
> do is probably apply the following formula to get each candidate's
> score.
> 
> Candidate's Score = Total No. of Ballots - Max wv against Candidate

That's close to what I was thinking.  I probably would, rather than using "total
number of ballots", use something that can be derived from the pairwise matrix,
which the total number of ballots isn't.

It would be nice if the score could be represented in a way that compares to
percentage, so that all scores add up to 100.  Then again, you could treat
"condorcet winner" as a score of 100, and any extra votes would push it above
100.  Non condorcet winners' scores might be "percentage of the votes necessary
to be the condorcet winner".

> If there is a Condorcet Winner, then I think it would be easiest to make
> that candidate's "Max wv against" equal 0.  This means that it is best
> to assume that a pairwise result of 0-0 between two candidates is a loss
> for both candidates.  Therefore, it would be best if any tie between two
> candidates is a loss for both the candidates.

Hmmmm, that doesn't sound right to me.
 
> If you think that this is a bit kludgy, then I suppose you could use
> MMPO (MinMax Pairwise Opposition).  This is basically the same as MinMax
> (wv) except that you "ignore" whether a pairwise result is a win or
> loss.  You just look at the number of pairwise 'votes' that oppose a
> candidate.

Yeah, I understand that there are advantages to that, but again, something
doesn't feel right about it to me.  It seems like you are throwing out valuable
information.  (I know throwing out valueable information is a necessity at times
to avoid worse effects, but still....something seems wrong with your description
to me.