It unfortunately keeps getting longer and more subvided. As of now there are 3 parts to the paper. I'm going to submit it to a journal pretty soon.
Part I: http://rangevoting.org/BestVrange.html Develops Bayesian Regret theory, finds BRs as closed formulas for a lot of voting systems, proves range voting superior to all rank-order voting systems (measured by BR) in 3-candidate elections under the RNEM (random normal elections model). Also finds the best ratings-based voting system for honest voters in 3-candidate elections (which is better than range voting, albeit only if over 91% or so of the voters are honest). Unfortunately about 50 pages long, but concisely summarized in table and plot. Part II: http://rangevoting.org/Best4.html Covers elections with more than 3 candidates. Shows range voting superior to all rank-order voting systems (measured by BR) in N-candidate elections under the RNEM (random normal elections model) for all numbers N with 3<=N<=9, for all honest+strategic voter mixtures. Again there is a table and plot which go a long way toward communicating the results even if you fail to read the rest of the paper. Part III: http://rangevoting.org/BestVot2.html Goes beyond the RNEM to consider other underlying probabilistic/political/utilities models, in particular "D-dimensional politics models," and based on either binary or continuum "issues." In the particular models discussed: * we can prove range voting is "optimal" in the binary model with honest voters, while various other voting methods are suboptimal * in the continuum model we can prove Condorcet methods are asymptotically optimal and superior to range voting. However (warning) all these results seem to depend sensitively on the precise definition of the underlying model; in contrast the results in parts I and II had been "robust." No previous paper was able to identify "best voting systems," using a valid measure (BR), in any reasonable underlying model. So in that sense, these papers are a breakthrough. Please email any comments / questions / etc to warren.wds AT gmail.com. -- 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
