[EM] Preliminary Range PAV results

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:
> Kristofer,
> 
> How about including Range SAV ?
> 
> Assume that the range ballots are functions from the set of candidates into the
> set [0, M], where M is the max possible rating.  Then ballot r contributes the
> following quotient to the total score for subset S of the set of candidates K:
> 
> Sum over k in S of r(k)
> 
>    divided by
> 
> Sum over k in K of r(k) .

That looks like a Range version of cumulative voting, and I think 
another said that it was as well. Just to be sure, I'll ask - is it 
Range cumulative voting?

If it is, it should be easy to handle. I also have implemented two 
STV-like Range methods and could give the results for those.

Surprisingly, CFC-Range (like CFC-Kemeny but with Range scores instead 
of Kemeny distance, and maximization instead of minimization), which 
I've also tested, is only very slightly more proportional than 
CFC-Kemeny at the cost of a lot of Bayesian regret, so CFC-Kemeny's good 
results aren't attributable to the linear programming concept alone.