[EM] General PR question

[Toby Pereira]

Normal Proportional Approval Voting would give it to ABC, ABD or ABE based on 
satisfaction. Everyone has voted for one of the elected candidates and some get 
two. Whereas with CDE, it's purely one each, but as you say this is envy-free. 
While I can see the merits of the envy-free argument, I would probably go for 
the ABC, ABD or ABE option. Perhaps a slightly weird analogy - you have an apple 
to give away on Thursday. John is the only person around, so you give it to him. 
Then on Friday you have two apples to give away. Fred is the only person to come 
along. You can give him one apple which would be envy-free, but the other one 
would get thrown away and wasted. Or you could give him both. But he might tell 
John who would then experience "envy". John doesn't materially lose anything by 
Fred getting two apples, so really I think Fred should get them both.

It's slightly different with voting, because the people who get the extra 
candidate could get more of their preferred legistlation through at the expense 
of the others - so it's not purely envy, but possible material loss. But where 
do you draw the line? Maybe I'll think of an example later but perhaps you could 
have a case where the only envy-free solution is for everyone to end up with 
much less representation than they would in the envy result. So would our ideal 
system be the one that flattens representation out as much as possible?




________________________________
From: Andy Jennings <elections at jenningsstory.com>
To: EM <election-methods at lists.electorama.com>
Sent: Fri, 22 July, 2011 19:42:06
Subject: [EM] General PR question

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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