[EM] Election Methods and DanceSport

[Xavier Mora]

I would like to submit to the consideration of the EM list a paper that 
I've written recently in connection with election methods.
I have made it available in  
http://mat.uab.es/~xmora/articles/iss2Aen.pdf .

The paper is not motivated by political elections, but by dancesport 
competitions. However, the problem is essentially the same, namely to 
combine several individual preferences into a global one.

At present, dancesport is using a system based on median ranks (called 
Skating System, because it was originally borrowed from figure 
skating). However, in the last years certain paradoxes have been 
observed, and some people have asked about the possibilities for a 
better system. Like in the case of political elections, in dancesport 
there is a strong reluctance to any deviation from the status quo. In 
spite of that, I have taken up the subject seriously and the result is 
the paper that I'm referring to.

After several initial attempts in other directions, finally I propose a 
method based upon ranked pairs.

In principle, the paper was addressed to dancesport people. So I try to 
keep the language as non-technical as possible. Even so, there are some 
parts that seem interesting also for more technical readers. In 
particular, I propose a method for converting the obtained ranks into 
more quantitative rates or quotas (based upon the information contained 
in the paired-comparisons matrix), which is a subject that was being 
debated in the EM list some months ago. On the other hand, I've 
included also a mathematical appendix where I give proofs of all the 
relevant properties of the version of ranked pairs that I'm using. As I 
say at the beginning of that appendix, many of the ideas of these 
proofs come from the original papers of Zavist and Tideman as well as 
the communications to the EM list and several websites related to it. 
However, sometimes I wasn't able to find exactly what I wanted or what 
I found was not clear enough. So, I finally decided to (re)produce the 
proofs by myself (which was more difficult than I expected).

I would appreciate very much any comments and suggestions.

Anyway, in writing this paper I've benefitted a lot from the EM list. I 
sincerely think that you are doing a great job.

Xavier Mora
puffinet at jazzfree.com