A couple of other possibilities for methods based on cycle proof conditions:
I. BDR or "Bucklin Done Right:" Use 4 levels, say, zero through three. First eliminate all candidates defeated pairwise with a defeat ratio of 3 to 1. Then collapse the top two levels, and eliminate all candidates that suffer a defeat ratio of 2 to 1. If any candidates are left, among these elect the one with the greatest number of positive ratings. II. SSCPE or "Six Slot Cycle Proof Elimination" Use six levels, zero through five. First eliminate all candidates with a pairwise defeat ratio of five to one. Then allowing only those ballot comparisons with strength 2 or greater (i.e. the preferred candidate is rated at least two levels above the other), eliminate all candidates with a defeat ratio of two to one. Then allowing only comparisons with strength three or greater, eliminate all candidates beaten with a defeat ratio of one to one, i.e. all defeated candidates. If there are two or more undefeated candidates, elect the one with the greatest number of positive ratings. III. SPE or Strong Preference Elimination: Use 2n levels. First eliminate all of the candidates that are defeated when the only ballot preferences counted are of strength n or greater, i.e. the rating of the preferred one is at least n levels greater than the rating of the other. If there are two or more unbeaten candidates, collapse the bottom three levels to zero, decrement the other levels by two, and decrement 2n to 2(n-1) and repeat the process recursively. The idea of SPE is that the most important eliminations are done by strong preferences, and weaker preferences are invoked only to break ties. More than one tie breaker step is needed only to ensure the technical compliance with Pareto. Random ballot could be used as a tie breaker just as well where ever voters are not allergic to it. ---- Election-Methods mailing list - see http://electorama.com/em for list info
