Kristofer Munsterhjelm asked me what "proportional representation" (PR) means.
At this time it is probably unwise to make a too-precise definition since every PR voting method seems to obey a different proportionality theorem. I say you should just assess each theorem on a case by case basis to see if you like it. But a somewhat imprecise definition is: I would say that any voting method which elects W winers from N candidates (arbitrary 0<W<N) with the property that "under an assumption of 'standard racist' voter behavior, it always elects the same proportions of different-'color' candidates as the voters (provided enough candidates of each color run) up to some reasonable error bound" is PR. However * what is the 'standard racist' voter behavior? * what are the 'error bounds'? (Once they get poor enough, they would no longer be acceptable, but I propose no precise threshhold) These differ from theorem to theorem. And for Asset Voting "standard racism" assumptions also are needed about the candidate-behavior. HERE'S MY LIST OF KNOWN PR VOTING METHODS: Webster, and certainly all "divisor methods" for party-list (it is one) already are known to obey such criteria. (The very definition of "divisor method" is a PR theorem.) This should include my new notion of "generalized divisor methods" where both multiplicative and/or additive parameters are involved. Hamilton-Vinton is one. See http://rangevoting.org/Apportion.html http://www.RangeVoting.org/NewAppo.html http://www.RangeVoting.org/BishopSim.html M.L. Balinski & H. Peyton Young: Fair Representation: Meeting the Ideal of One Person, One Vote (2nd edition), Brookings Institution Press 2001 Asset voting also obeys a PR theorem. http://rangevoting.org/Asset.html paper #77 at http://www.math.temple.edu/~wds/homepage/works.html RRV also (RRV is kind of based on "stealing" the divisor-method idea, inside). paper #78 at http://www.math.temple.edu/~wds/homepage/works.html http://rangevoting.org/RRV.html Hare/Droop STV also. Nicolaus Tideman: The Single transferable Vote, J. Economic Perspectives 9,1 (1995) 27-38. And LPV(kappa) ("logarithmic penalty voting") also. Invented by F.Simmons. Described in paper #91 at http://www.math.temple.edu/~wds/homepage/works.html Also certain PR methods which are "precinct countable" invented by Forest Simmons, see puzzle#15 at http://rangevoting.org/PuzzlePage.html . Finally, there was also a simple one invented by a student at University of Michigan named Tim Hull. See http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-April/020194.html http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-April/020195.html That's my list. Is anybody aware of any other PR methods? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
