>> Warren defines BR in such a way that Range is unbeatable >> given sincere votes. > Absolutely...
--Sorry: these claims, although stated with the utmost apparent confidence by their authors, are utterly false. Range voting is beatable, and has been beaten, with honest voters -- and I was the one who did that! Consult paper #101 here http://www.math.temple.edu/~wds/homepage/works.html e.g. see the plot http://www.math.temple.edu/~wds/homepage/BestVrange.html#RegPlot and the table http://www.math.temple.edu/~wds/homepage/BestVrange.html#BigResultsTable and note that the BRBH (best ratings-based voting system for honest voters, which I explicitly derive in the 3-candidate RNEM case) does beat plain range voting, with 100% honest voters, having BRBH regret = 0.067454 versus Range Voting Regret = 0.096864 = 1.436*BRBHregret. Further, certain systems also beat range voting with *strategic* voters, for example range+top2runoff system with 2 rounds beats plain range (i.e. has lower BR) if there are about 75% or more strategic voters in the mix. Do these imply that we should abandon range voting? At present, I do not think so, and here's why. BRBH does beat range, but only if the honesty-fraction in the electorate exceeds 91%. And the regret reduction is fairly small. If however, we have only a small fraction of sincere voters, range is greatly superior to BRBH (by a lot more than a factor of 1.4). Range+top2runoff does beat range if the strategy-fraction is large, but it doesn't beat it by much (10-30% regret reduction); meanwhile range beats range+top2runoff by a lot more than that if the honesty-fraction is large. And both BRBH and range+top2runoff are a lot more complicated than (and harder to "sell" than) plain range voting. So in view of this, at present I still think plain range voting is a pretty good choice. -- 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
