[EM] Proportional Representation beyond STV?

[Alex Small]

James Gilmour said:
> If you looked at this from the elector's perspective I think you might
> propose a different taxonomy and perhaps have a different final
> preference.

Quite true.  I guess you could classify PR methods as either party-based
or candidate-based, but I divided the candidate-based methods into two
categories for technical reasons.  As to whether some candidate-based
methods can accurately be described as generalizations of single-winner
methods, you say:

> As an aside, I would question whether you are right to describe STV-PR
> as a generalisation of a single-winner method (IRV).  Both use
> transferable, preferential voting, and they share a number of defects,
> but STV-PR involves an essential process (transfers of surpluses) than
> cannot occur in IRV, so I suspect the two are qualitatively different.
> Alternatively, IRV might be considered a special case of the use of STV,
> a limiting application of STV when n=1.

You more or less make my point here.  STV-PR can be thought of as IRV
augmented with a fractional transfer process, or IRV can be thought of as
STV when n=1.  Whether you want to call that a "generalization of a
single-winner method" is more a semantic issue.  There's a clear kinship
between IRV and STV, just as there's a clear kinship between Approval
Voting and Proportional Approval Voting.  Sure, the plurality group
(Cumulative Voting, SNTV, Limited Voting) reduces to a single-winner
method when n=1, but I made the additional distinction between "fractional
methods" involve transfer of fractional votes (STV, PAV, etc.) and methods
without fractional transfers.

So I stand by my categories of "fractional methods", "plurality methods",
and "list methods."



Alex