[EM] Divisiveness measures

[Daniel Carrera]

On Mon, Jul 25, 2022 at 5:51 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> 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?
>


For any ranked method, a natural score for each candidate is their rank
normalized by the number of candidates.

I don't like using standard deviations for anything that is not known to be
Gaussian. Even other bell curves can really mess up the stdev. MAD is
better, and it's reasonably intuitive ("half the points are at most this
far from the median"), but I'm boring and I like quantiles.

Divisive Score = (95th percentile approval score) - (5th percentile
approval score)

or

Divisive Score = (85th percentile approval score) - (15th percentile
approval score)


Cheers,
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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