[EM] What does "proportional representation" MEAN? And list of known PR methods (know any more?)

[Warren Smith]

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