Forest and I were discussing PR last week and the following situation came up. Suppose there are five candidates, A, B, C, D, E. A and B evenly divide the electorate and, in a completely orthogonal way, C, D, and E evenly divide the electorate. That is:
One-sixth of the electorate approves A and C. One-sixth of the electorate approves A and D. One-sixth of the electorate approves A and E. One-sixth of the electorate approves B and C. One-sixth of the electorate approves B and D. One-sixth of the electorate approves B and E. It is obvious that the best two-winner representative body is A and B. What is the best three-winner representative body? CDE seems to be the fairest. As Forest said, it is "envy-free". Some methods would choose ABC, ABD, or ABE, which seem to give more total satisfaction. Is one unequivocally better than the other? I tend to feel that each representative should represent one-third of the voters, so CDE is a much better outcome. Certain methods, like STV, Monroe, and AT-TV (I think) can even output a list of which voters are represented by each candidate, which I really like. I also note that if there was another candidate, F, approved by everybody, it is probably true that ABF would be an even better committee than CDE. Is there a method that can choose CDE in the first case and ABF in the second case? Andy
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