Re: [EM] multiwinner election methods
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.htmlpaper #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 However this paper is out of date and not fully satisfactory... 2.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... Election-Methods mailing list - see http://electorama.com/em for list info
[EM] multiwinner election methods
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.htmlpaper #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 Election-Methods mailing list - see http://electorama.com/em for list info
