Juho: In your explanation of "minimizing violated pinions", you described your own interpretation of proportionality.
If you're interested in proportionality, the matter of optimally equal representation per voter, I've told you where to read about it. If you're interested in minimizing violated opinions, then PR is not for you. If I were doing PR, I'd be glad to instruct you in proportionality. And, if so, I'd be glad to walk you through the subject and and explain to you your specific errors. But, as I said, I no longer do PR. As it is, I can only refer you to the sources that I cited. Read them conscientiously, and don't cling to your assumptions. It's arrogant to believe that you're more qualified in a subject, when you don't want to take the time to study it. Don't cheat yourself in that way. That's my best advice for you. Now, forgive me if I say a few things that I've already said. I'm saying it with other things that I haven't said. For allocating seats to parties: I used to prefer Sainte-Lague (as recently as earlier in this discussion), because I felt that if you want PR at all, then you might as well get the best pure proportionality. Also, I guess I was influenced by others, who believed that the Repubs & Dems would remain the big 2, and wanted the small parties to get their fair share. I bought into that feeling. But I have more confidence in the voters than that. That's why I prefer single-seat districts, or at least the use of a good single-winner method instead of PR. I believe that if some of the small parties are better, then they won't remain small for long, when Approval is in use. But, as I said, I have nothing against PR--I just don't consider it necessary at all. But of course PR would be a lot better than Plurality or Runoff. I'm convinced that if the voters can support what they really like, then there will be all the improvement we could ask for. As I said, PR isn't viable here anyway, because it's a drastically different notion of representation and govt--whereas a better single-winner method is nothing other than a better way of doing what we already do--electing candidates to single-member districts. Because I don't consider PR necessary anyway, For allocating seats to parties, I now prefer d'Hondt, with its balance between proportionality and majoritarianism. (and, for STV, the Droop quota, for the same reason). Someone who doesn't consider PR necessary at all has no reason to insist on the purest all-out un-compromised Plurality of Sainte-Lague. But it just depends on what you want. I have no criticism of Sainte-Lague, or for the goal of optimally equal representation per person that requires Sainte-Lague. In fact, as I said, any of the PR systems and methods would be fine. Allocating seats to districts: That's a whole other ballgame. For that application, there's really no room for debate. Living in a some particular district is very different from preferring an unpopular party. If the party that you like best is unpopular, then that's the way it goes. But, regardless of which district you reside in, you have an obvious right to equal representation. To the greatest extent possible, you have a right to as much representation as anyone else. That's why Sainte-Lague is the way to allocate seats to districts. When allocating seats to districts, the question is: Do you or do you not want as much representation as the other people? If so, then the answer is Sainte-Lague. But, if you're happy with avoidably less representation than other people have, that's your business, and it isn't for me to tell you what you should want. Mike Ossipoff ---- Election-Methods mailing list - see http://electorama.com/em for list info