[Election-Methods] proportional representation, recent questions and older work

[Warren Smith]

> To my understanding, RRV is constructed so that it reduces to D'Hondt if
> people stick to party lines and vote max for all within the party and min to
> the rest. Is that true?

--there is a parameter in RRV that can be adjusted so we get D'Hondt
with one value and Sainte-Lague with
another (and a continuum of values of the parameter is permitted in between).
You [Kristofer Munsterhjelm] could e.g, adjust it to maximize
performance on your test.
The RRV paper was
     http://www.math.temple.edu/~wds/homepage/works.html  #78

However I warn you re your test that many people believe that somewhat
NONproportional representation is better and indeed some of the
apportionment methods were developed with that idea in mind (e.g.
Jefferson "offers incentives for parties to merge").
CRV web pages on apportionment include
    http://www.rangevoting.org/Apportion.html
    http://www.rangevoting.org/NewAppo.html
    http://www.rangevoting.org/BishopSim.html

Who is right about that?  Well, Jobst Heitzig is quite right that what
matters is not the composition
of the legislature per se; it is the result of votes in that legislature.
I had the same insight some time ago
and used it to propose a method of evaluating MULTIwinner voting systems via
BAYESIAN REGRET methodology
(formerly, BR only was applicable to single-winner voting methods,
so this would be groundbreaking extension).

That proposal is sketched here:
    http://groups.yahoo.com/group/RangeVoting/message/7706
The original BR frameowrk for single-winner systems is discussed here
     http://rangevoting.org/BayRegDum.html

But so far multiwinner-BR has never actually been tried, because I
lacked the time.

There supposedly is a paper-in-progress by me and Forest Simmons which
is a review and comparison of multiwinner voting systems.  It may
never get done.  Anyway, I originally wrote
the paper which is available here
    http://www.math.temple.edu/~wds/homepage/works.html  #91
but that version is already well out of date. Forest Simmons had
actually invented quite a lot of the stuff in that paper independently
(I found out later)  and then he solved an open problem posed in the
paper (about finding a multiwinner voting system achieving the
best-possible combination of the properties discussed there).
Simmons's solution of that problem is discussed here
    http://rangevoting.org/PuzzlePage.html#p15

Also in the meantime I invented the extension of the BR framework to
multiwinner systems, and some new multiwinner voting systems and
properties were invented.
The plan then was to rewrite the paper now jointly to do all that.

Finally I now see Kristofer Munsterhjelm has begun his own
investigations along the same lines.

> Perhaps RRV could work better  by somehow using your new
> apportionment method instead of Sainte-Laguë.

--that's an interesting idea;
There might be ways to generalize RRV to emulate all kinds of other
apportionment methods.
If you work out how to do that, please explain.

-- 
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking "endorse"
as 1st step)
and
math.temple.edu/~wds/homepage/works.html