[EM] Median-based PR systems

[Toby Pereira]

In Forest Simmons's system of Proportional Approval Voting each voter's satisfaction score is based on the number of elected candidates they voted for - 1 + 1/2 + 1/3 + ... + 1/n and the set of candidates giving the highest mean satisfaction score wins. This could be changed to highest median. (Other versions such as 1 + 1/3 + 1/5 etc can be used.)
 
As I think has been dicussed in this mailing list, this can be extended to Range Voting by using harmonic numbers which give a continuous function for summing reciprocals. If you gave three elected candidates 3/10, 4/10 and 9/10, the number of elected candidates that you voted for would be considered to be 0.3+0.4+0.9=1.6. As before you could find the set of candidates with highest median satisfaction score.
 
Toby
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