[EM] Condorcet Flavored PR Methods

[Forest Simmons]

On Mon, 30 Sep 2002 matt at tidalwave.net wrote:

> On 28 Sep 2002 at 16:17, Markus Schulze wrote:
>
> > Dear Forest,
> >
> > you wrote (27 Sep 2002):
> > > A "Condorcet Flavored PR Method" is an M-winner election method that
> > > (1) compares candidate subsets of cardinality M head-to-head, and
> > > (2) does the comparison in such a way that the winning combination
> > > of any head-to-head comparison provides better PR representation
> > > than the loser subset, and
> > > (3) gives the win to the "beats-all" combination if there is such
> > > a subset.
> >
> > Tideman has proposed such an election method:
> >
> >     T. Nicolaus Tideman, Daniel Richardson,
> >     "Better Voting Methods Through Technology: The
> >     Refinement-Manageability Trade-Off in the Single
> >     Transferable Vote," PUBLIC CHOICE, vol. 103,
> >     p. 13-34, 2000 (http://www.econ.vt.edu/tideman/rmt.pdf)
> >
> I doubt that CPO-STV consistently gives the winning outcome "better PR
> representation" than the losing outcomes.  It only transfers votes when at least one
> candidate is common to both outcomes.  Since it is the transfer that makes it PR
> and since the proportion of outcome pairs that have common candidates decreases
> as the number of candidates increases relative to the number of winners, it seems
> to me that CPO=STV is semi- or quasi-PR.
>
> Another way to compare outcomes is to count all pairwise candidate winning votes
> between the two outcomes, substituting approval count for winning votes when the
> two candidates being compared are the same candidate thus favoring those
> outcomes with candidates that have high approval counts.

Does either CPO-STV or the alternative proposed by here by Matt satisfy
the "proportionality for solid coalitions" property mentioned in the paper
by Tideman and Richardson?

Here's the definition given for this property:

"If there is a set of voters, V, who rank all candidates in some set, S,
ahead of all other candidates, then the number of candidates in S who are
elected will be at least as great as the proportion of the electorate who
are in V multiplied by the number of candidates to be elected, rounded
down to an integer (provided that S contains at least that many
candidates)."

Forest

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