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

[Raph Frank]

On Tue, Nov 17, 2009 at 5:02 PM, Warren Smith <warren.wds at gmail.com> wrote:
> 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)

I am not sure referring to "racism" is a good plan :).

Something like

"Any group representing more than N/M of the voters, where M is the
number of seats to be filled, must be able to guarantee that N of
their candidates are elected (assuming they run enough candidates)".

I think all PR methods meet this (as it is the Hare quota).

Also, a reasonable definition for ranked methods is:

http://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions