[EM] Divisiveness measures

[Kristofer Munsterhjelm]

A while ago, a community I often visit (http://museumofzzt.com) ran a 
game creation contest where the objective was to create the best game in 
144 minutes.

The judges, who were also the game creators, chose the winner by the 
Borda count 
(https://museumofzzt.com/file/view/summer22bkzzt/?file=Results%2FOverall%20Results.png 
).

One interesting bit about this, from a voting perspective, is that they 
also calculated a divisiveness score per candidate, which provides 
information about how consistent that candidate's rank is. They used the 
mean absolute deviation (the most obvious choice would be the MSE, but 
perhaps the MAD is better since it's more robust).

It's an interesting concept. For Borda and Range it's pretty easy: use 
some variance or robust variance measure. But figuring it out for 
Condorcet methods seems much harder.

A possible quick and dirty version could go like this: For any method 
where the candidate that maximizes or minimizes some score is elected, 
use bootstrapping to create a distribution of that score, per candidate. 
Let the divisiveness measure be the standard deviation (or some other 
dispersion measure) of a random variable of that distribution.

It's not particularly elegant, however! Any better ideas?

-km