[EM] multiwinner election methods

Warren Smith warren.wds at gmail.com
Sun Oct 12 11:00:18 PDT 2008


1. the right way to compare election methods is "Bayesian Regret" (BR).
http://rangevoting.org/BayRegDum.html

For a long time I thought this was only applicable for single-winner
voting methods.
However, I eventually saw how to do it for multiwinner methods also:
 http://groups.yahoo.com/group/RangeVoting/message/7706

it would be a substantial computer programming project to try to do
this, and so far, nobody
has undertaken that project. But I recommend it!!  If Gregory Nesbit
is looking for
a project to undertake for, e.g. Intel Science Talent Search, he could do it :)

In the absence of BR, one is reduced to comparing voting methods using
"properties."
I also recommend that, but for multiwinner voting methods this too is
in its infancy.
A paper attempting to compare multiwinner voting methods (using properties)
by me is here
 http://www.math.temple.edu/~wds/homepage/works.html    paper #91.
However this paper is out of date and not fully satisfactory...

2. About RRV (reweighted range voting)
http://rangevoting.org/RRV.html
recent developments are these:
Steven J. Brams found an example (in email to me) in which RRV
violates "favorite betrayal."
That is, there are elections in which foolishly voting your true
favorite top, causes you
to get a worse election result.

Warren Schudy found a beautiful theorem that EVERY multiwinner
election method in
which the ballots are approval-style or range-style, must either
  1. fail to be proportional
  2. fail to be "invariant to reinforcement" (IR).

IR means that if a ballot is altered to increase score for X, that
should not stop X winning;
similarly if decrease score for X, that should not stop X losing.

This Schudy result basically explains the Brams example, explains my
own example where
RRV fails a multiwinner analog of "participation criterion," and shows
that apparently these complaints
about RRV are not really complaints because EVERY voting method would
be subject to
those complaints (at least if based on these sorts of ballots and
proportional).
I can't fully explain all that here.

3.  I would like to improve my out of date paper #91 and allegedly
Forest Simmons and I are going to do so.
But we've been alleging that for about 2 years...

The improved paper will include more multiwinner voting methods, more
properties, and more theorems.
A fair number of new mltiwiner methods have been suggested on this and
other internet forums which
unfortunately were not examined in my paper #91.
Schudy told me he is not so hot on asset voting and doesn't like the
"representativeness" property
in that paper.  I agree on the latter and partly agree on the former.

Still, at the present moment my recommendation as a voting system would be
* if 1-winner: use range voting
* if more winners: use asset voting.
* if asset cannot be used... unsure...  perhaps RRV.

Incidentally, Forest Simmons solved the open problem in my paper #91
by inventing new
voting systems obeying the maximum possible set of the properties in that paper.

4. systems based on every subset of the candidates is a
"pseudocandidate" are just nonstarters
because there are far too many pseudocandidates.


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



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