>> It's an interesting question whether there can be a proportional >> multiwinner voting method >> without needing to use "reweighting"... but this is not it. "Asset >> voting" works >> http://rangevoting.org/Asset.html >> but it is "unconventional."
--Actually, now that Kris.Munk. points out "combinatoric" methods, I recall that "penalty function" methods with cleverly chosen functions can indeed work. You consider all binomial(C,W) possible winner-sets, where C=#candidates, W=#winners, 0<W<C, and for each you evaluate a function. The set with the greatest (or least, depending on your defn) value of the function wins. The function has to be defined very carefully, but it is possible to do so in such a way that you can prove a proportionality theorem. (If you just try any old definition, it will almost certainly fail to yield proportionality.) If you look at my paper #91 here http://www.math.temple.edu/~wds/homepage/works.html (which is out of date and needs to be improved/revised - Forest Simmons and I were planning on doing that... maybe there should be other authors too like KM himself perhaps...) then you will see the LPV method (logarithmic penalty voting) basically invented by Forest Simmons, does the job. See section 7.9. LPV is a beautiful idea, but its "representativity" property actually is probably not a good thing (we have some results indicating it conflicts with other properties) and also problem with this and every other "combinatoric" method (at least if implemented by brute force) is binomial(C,W) can be huge, causing enormous work by the election authority. It may be that "branch and bound" methods can cut this work down to acceptable levels, but that is not yet confirmed experimentally. Also in stupider combinatoric methods where voter needs ot specify that many bits of info in her vote, it would be even worse. -- 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
