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<TITLE>Old topic: Finding the "most representative" ranked ballot</TITLE>
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<P><FONT SIZE=2 FACE="Arial">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.</FONT></P>
<P><FONT SIZE=2 FACE="Arial">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.</FONT></P>
<P><FONT SIZE=2 FACE="Arial">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.</FONT></P>
<P><FONT SIZE=2 FACE="Arial">The results of my test for 2007 D-1 baseball are at </FONT><A HREF="http://www.kislanko.com/tau_dist_pw_1.html"><U><FONT COLOR="#0000FF" SIZE=2 FACE="Arial">http://www.kislanko.com/tau_dist_pw_1.html</FONT></U></A>
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<P><FONT SIZE=2 FACE="Arial">Paul Kislanko</FONT>
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