Warren Smith wrote:
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However this paper is out of date and not fully satisfactory...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.
Does that include multiwinner methods that are based on ranked ballots?
I'm not sure, because on one hand, you only specify approval and range
style, but on the other, any range ballot can be reduced to a ranked
ballot with some additional information (how much better a certain
choice is to another), and so one could construct a rated pseudo-ballot
by running a ranked ballot through a weighted positional system.
I guess the theorem applies neither to asset (unless candidates pledge
to transfer support in a certain way) nor to closed list PR, since both
use single-vote type ballots.
4. systems based on every subset of the candidates is a
"pseudocandidate" are just nonstarters because there are far too many
pseudocandidates.
Some of these might work if they have a single local optimum, so that a
hill-climbing algorithm can find that optimum. But then it could be
restated by including the hill-climbing algorithm into the method, and
so might be exempt...
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