# [EM] Multi-seat Condorcet

James Green-Armytage jarmyta at antioch-college.edu
Mon Aug 16 00:30:56 PDT 2004

```>Does anyone know of a multiple-seat election method that yields
>proportional representation if the number of seats is large and the
>Condorcet winner if there's only one seat? Such a method would likely be
>better than STV for small (<10) numbers of seats since IRV's flaws
>probably extend to STV, though a lesser extent. It would also be helpful
>to defuse the argument that IRV is better than Condorcet because it allows
>the same system to be used for multi-winner and single-winner elections.
>-wjs

Yes! This method you speak of is known by the faithful as CPO-STV, which
stands for comparison of pairs of outcomes by the single transferable
vote. Its inventor is Nicolaus Tideman.
Here is the link to a great paper by Nicolaus Tideman and Daniel
Richardson, which traces the history of STV and defines CPO-STV as a part
of that history:

http://www.econ.vt.edu/tideman/rmt.pdf

The definition of CPO-STV in this paper is a bit terse, so here is the
link to my own attempt to explain CPO-STV, which goes a lot slower and
gives a detailed example:

http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting_methods/survey.htm#cpostv

As a bonus, I will give you a super-short definition of CPO-STV here.
Where single-winner Condorcet does pairwise comparisons between individual
candidates, CPO-STV does pairwise comparisons between total outcomes, that
is, possible ways for all the seats in a multi-member district to be
filled.
How do you compare outcomes?
1. Set aside candidates not in either outcome, and transfer their votes to
the remaining candidates.
2. Only transfer surpluses from candidates who are in both outcomes.
3. Now, each candidate has been assigned a certain number of votes. Find
the score for each outcome simply by adding up the votes held by each
candidate in that outcome. Whichever outcome has the higher score, wins
the comparison.
Thus, CPO-STV can construct a pairwise matrix between possible outcomes.
Use this matrix to find the winning outcome, according to whichever
Condorcet completion principle you prefer.
CPO-STV is more computationally expensive than most other voting methods,
but it is possible to save a lot of computing by using shortcuts, which
can make it unnecessary to calculate many of the entries in the matrix.

my best,
James Green-Armytage

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