[EM] Preliminary Range PAV results

[Kristofer Munsterhjelm]

Jameson Quinn wrote:
> Can you add a range-STV method? This would reweight ballots for elected 
> candidate X by:
> 
> max(0,(N-D(rN/R))/N)
> 
> where N is num voters, D is droop quota, r is ballot's range score for 
> X, and R is electorate's range total for X. This should be simple to 
> code, a small variant on greedy PAV with a different reweighting formula.
> 
> This is a more STV-like method, in that it elects candidates in order of 
> some pseudo-"strong to weak", not in a proportional order as does greedy 
> PAV.

If N = total number of voters, then (unless there's a bug somewhere) we get:

PA_Linear_Range_STV                                 0.29813 0.00031

If N = the number of voters voting according to the ballot being 
reweighted, then the result is:

PA_Linear_Range_STV                                 0.20928 0.01991

As a comparison:

PA_Maj[Cardinal-20]                                 0.31348 0
PA_STV                                              0.11902 0.10007
PA_DHwL(L-R_offense/1/(wv),_0.925)                  0.20924 0.02172

The first is Range, and the second is ordinary STV. The third is the 
closest ranked ballot method at this level of proportionality.

If you suspect a bug, I could give examples where "N = size of entire 
electorate" gives a disproportional result (according to my program). "N 
= number voting this way" seems more well behaved, but if you're 
interested, I could also give an example where it differs from STV 
and/or Birational.