Multi-seat Condorcet

[Warren Schudy]

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

/-----------------------------------------\
| Warren Schudy |
| WPI Class of 2005 |
| Physics and computer science major |
| AIM: WJSchudy email: ***@wpi.edu |
| http://users.wpi.edu/~wschudy/ |
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[James Green-Armytage]

Post by Warren Schudy
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/~***@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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[Steve Eppley]

Hi,

Post by Warren Schudy
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.

James G-A has already posted a reply containing a
link to Tideman's Condorcet/PR method so I won't
repeat it.

Another method that appears to meet Warren's spec is
a variation of STV that never eliminates a Condorcet
winner. Or that, when eliminating a candidate,
eliminates the candidate that ranks lowest in
the MAM social ordering.

I'm sorry to take a contrarian position I don't have
the time to defend, but I'd like to add that I don't
find the argument for PR compelling when PR is compared
to the best alternatives. Consider these alternatives:

1. (For electing a large legislature, too large for
the voter to rank individual candidates. A quasi-PR
system.) Voters rank parties, not candidates.
Each voter ranks the parties in order of preference.
Each party is awarded seats in proportion to the number
of voters who ranked it topmost, except a lot of extra
seats are awarded to the party that would win if the
votes were tallied by a good single-winner system
(e.g. MAM). (The other exception is that, like in STV,
votes for parties that are too unpopular to reach
some threshold would count for their second favorite
parties, etc.) In addition, the party that's
awarded the extra seats is also given the power
to unilaterally set the legislature's agenda and
a veto over rule changes, and if a parliamentary
system, a veto over the selection of cabinet
officers (including prime minister).

2. (For electing a small legislature, small enough
that each voter can rank most of the candidates.
An utterly non-PR system.) Each voter ranks the
candidates in order of preference. The N candidates
atop the MAM social ordering are elected.

I call a legislature "representative" if the policies
it adopts are similar to those the people themselves
would adopt if they had time to deliberate and vote
directly on the issues using a good voting method.

After a PR legislature is elected, the members still
need to reach compromises, so I think the policies
they adopt would tend to be similar to the policies
that would be adopted using either alternative,
and similar to those the people themselves would
adopt if the people could deliberate and vote
directly. I see two key differences:

1. The effects of vote trading, which would occur
most with PR and least with alternative #2. I can't
predict whether the extra vote trading under PR
will be a net gain or loss for society.

2. I'm concerned that voters whose favorites aren't
centrist won't pay much attention to their favorites'
positions on the various centrist compromise policies
that can pass the legislature, leaving too much room
for their favorites to be unaccountable and therefore
more corrupt.

--Steve
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