[EM] General PR question

[mrouse1 at mrouse.com]

It looks very nearly a tie, which complicates things. :)

In the weighted proportional method I described in another email, the
results would be (for a slate of 3 candidates, and ten votes for each pair
mentioned in the problem).

ABC = 60
ABD = 60
ABE = 60
ACD = 50
ACE = 50
ADE = 50
BCD = 50
BCE = 50
BDE = 50
CDE = 60

The possible winning slates are ABC, ABD, ABE, and CDE. So it picks the
same groups as mentioned before. Not much help there.

If we look at each winning group, A and B appear in three possibilities,
while C, D, and E appear in 2 apiece. So it seems reasonable to make sure
that the winning group has both A and B in it. If we are limited to 3
people, that leaves one spot.

So flip a fair 3-sided coin, and pick the third winner. :)

Mike

PS with a weighted system, A would get 25 votes (out of 60), B would get
25, and (C,D, or E) would get 10. Of course, in a 3 person legislature,
this is equivalent to giving each the same power, since any two could
outvote the third.




> 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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