[EM] Old topic: Finding the "most representative" ranked ballot

[Paul Kislanko]

I forget who posed the question, but in my work with ratings for sports, I
found a use for "Kendall's tau distance", and that could be helpful.

For each pair of ballots just count the number of swaps that a bubble sort
would require to sequence either of the ballots the same as the other. (This
number is also the count of what are called "discordant pairs").. The
calculation is O(2) for number of alternatives for each comparison of 2
rankings, and the results comparison is O(2) for number of ranknigs.

In the attachment I use tau distance to validate that my composite of 5
computer rankings was most representative by summing the tau distances for
it and each of the five constituent rankings, and ordering the list of
rankings by descending total tau distance. It seems to me that this would be
useful test for criteria compliance, or even as a meta-criterion for
comparing methods that have an ordered list as their result.

The results of my test for 2007 D-1 baseball are at
http://www.kislanko.com/tau_dist_pw_1.html

Paul Kislanko

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