[EM] Phragmen proportional representation for range voting

Ross Hyman rahyman at sbcglobal.net
Sun Jul 2 05:25:09 PDT 2017

The rating of the mth elected candidate on the ith ballot is v(i,m). 
The minimum value that v(i,m) can take is 0 and the maximum is 1.
The nth elected candidate is the one that minimizes the following:
s(n) = (sum(m = 0 to n-1)p(m;n)s(m) +1)/v(n)
where s(0)=0.
v(n) = sum(i)v(i,n) 

p(m;n) for approval is the number of ballots that approve of candidates m and n and none of the candidates between m and n.  

The natural generalization for range voting when interpreting the v(i,n) as probabilities is

p(m:n) = sum (i)v(i,m)v(i,n)product(j = m+1 to n-1) (1 – v(i,j))

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