[EM] VoteFair representation ranking recommended for Czech Green Party

[Kristofer Munsterhjelm]

VoteFair at SolutionsCreative.com 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.