[EM] Divisiveness measures

[Kristofer Munsterhjelm]

On 7/25/22 11:33 PM, Daniel Carrera wrote:

> 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)

You're right, that makes a natural choice, and for range and approval, 
it's also rather easy (like Borda).

I was just playing with the idea that if the method can be cast as 
"elect max over c in Candidates: f(c)", then a natural choice is also 
some kind of dispersion based on f, so that the method is consistent in 
that sense.

-km