[email protected] wrote:
Once again Markus Schulze is trying to discredit the Condorcet-Kemeny
method. (See below.)
This is ironic because "his" method -- which he calls the Schulze
method, and which would more meaningfully be called the
Condorcet-Schulze method -- produces the same results as the
Condorcet-Kemeny method in most cases.
What percentage of cases produce the same overall ranking sequence? I
would guess it's at least 85% to 90%, and perhaps as high as 95%, if all
possible ranking combinations are considered. If only the single-winner
result is considered, the results would match in an even higher
percentage of cases.
If Schulze and Kemeny produces the same result so often, why not just
switch to Schulze and gain clone independence and polynomial runtime?
Independence of clones seems more important than Kemeny's unique
Reinforcement criterion anyway.
If the answer is, as you hint later, that Kemeny somehow produces better
outcomes than Schulze in the cases they do differ, how would you
quantify better? Perhaps there's a better method still than Kemeny, say
a method that is at least as good on average and satisfies clone
independence (or perhaps IPDA, etc).
For those who may not know, and especially for Peter Zbornik to whom
Markus intended his message, there is a third similar method. It's
called Ranked Pairs on Wikipedia, it's sometimes called the Tideman
method, and a more meaningful name would be the Condorcet-Tideman method.
The Condorcet-Schulze method and the Condorcet-Tideman method use a
similar elimination approach, where one looks for the biggest pairwise
numbers and the other looks for the biggest margins of victory.
Not necessarily. The beatpath approach (count number of stronger
beatpaths between all pairs of candidates - the winner is the one with
no stronger beatpath to him than away from him) doesn't involve elimination.
(Other Condorcet methods do not have characteristics that make them
worth considering in real elections. One of them is used in games where
its element of randomness adds entertainment value.)
Of note, one could mention Copeland (in sports) and a standard
elimination tournament (which, when used with the same ballots, is
Condorcet). You're right about these, though; the former isn't
cloneproof and the latter is very susceptible to strategy.
This is a good time to mention that there is an organization (I don't
recall the name) that calculates the Condorcet-Schulze winner and also
calculates the Condorcet-Tideman winner. If these are not the same
candidate, the Kemeny scores are calculated for the two applicable
sequences, and the sequence with the higher Kemeny score determines
which of the two candidates is declared the winner. This is a clever
way to get around the challenge of writing software to calculate the
Condorcet-Kemeny method. It also demonstrates the similarities between
the results calculated by the Condorcet-Schulze and Condorcet-Kemeny
methods. Furthermore, it demonstrates that the person behind it is wise
enough not to completely rely on the Condorcet-Schulze method.
That would be Condorcet with dual dropping, and the organization is the
MKM-IG: http://www.mkm-ig.org/ . I think Schulze said the method might
not necessarily be cloneproof: the idea would be something like that in
the base scenario, the Schulze winner is best, but then, when you
introduce (or remove) a few clones, the Tideman winner becomes "better"
and so it switches.
For perspective: Back around 1990, without knowing the names of voting
methods and voting criteria, I was figuring out the fairest voting
method. After I considered and dismissed the IRV approach, I considered
and then dismissed the Condorcet-Schulze approach, which is to look at
the biggest or smallest pairwise numbers. I reasoned that that approach
has the same weakness as IRV and plurality. Whereas plurality and IRV
look at first-choice preferences, the Condorcet-Schulze approach is
better because it looks at pairwise numbers. But I knew that looking
for the biggest or smallest numbers is like looking at the surface of
water to figure out what's happening beneath the surface. I reasoned
that a fair method needed to look deeper. So I used an approach that is
similar to fitting a straight line through a number of non-aligned data
points, namely to add together numbers that measure the degree of fit.
The resulting sum -- which in this case is of applicable pairwise counts
-- provides a way to find the best fit by finding the sequence with the
maximum sum. It was years later that I found out that an academically
known method (the Kemeny method) similarly used the sum of opposition
(!) pairwise counts and looked for the smallest such score. This
parallel development should not seem too surprising because the general
approach is used in yet other situations in physics and mathematics.
Maybe you would find my CFC-Kemeny multiwinner method less arbitrary
than "elect and reweight", in that case. The method basically picks k
orderings (for k seats), where no one candidate appears in first place
in more than one ordering. It assigns each ordering to a group and
divides the ballots (fractionally, if so needed) among the groups so
that the sum of each group's Kemeny score is maximized, subject to that
each group contains an equal fraction of the electorate; and it then
selects the set of orderings which maximizes this sum of Kemeny scores.
The allocation of votes to groups can be done using linear programming
because once the orderings have been set, the Kemeny scores for each
voter are known.
Because the method has to go through almost every ordering (not just
every candidate) for each group, it has a really bad runtime - only
suitable for small councils and numbers of candidates. The limitations,
as well as it being based on Kemeny, has led me to consider other
approaches; but the method itself is quite proportional and it is
Kemeny-like.
----
Election-Methods mailing list - see http://electorama.com/em for list info
