I'm not sure about rankings, but Warren's extension to ratings is neat and straightforward.
Rivest mentions that his three ballot checker machine would have to enforce the single-vote plurality rules as an extra check that could just be removed, losing nothing of the benefits of three-ballot. Also, just as Approval is a two value rating summation system, three ballot extends naturally when moving beyond two values of rating. Rivest explains at one point that the candidates all get between n and 2n marks for n voters. The traditional "vote" count is the counted marks minus n. In the same fashion, Warren has extended the ballot so that all candidates get between r*n and 2*r*n rating vote for a max rating of r and n voters. Subtract off r*n and you have the secure rating vote. Cool, huh? http://rangevoting.org/Rivest3B.html The down side is that since this directly accomplishes summation of the ratings, per-ballot-rating methods such as IRNR and raking-derivation to Borda or Condorcet/VRR are not possible. Brian Olson http://bolson.org/ On Fri, 29 Sep 2006, [EMAIL PROTECTED] wrote: > Very interesting method. Just a quick question. The article mentions that > rank-order methods would be really tough to do. Wouldn't the method just > be two votes with the correct rank-order and one with the reverse order? > If you wanted A>B>C, you'd have two votes for that and one for C>B>A. > Borda would end up with the score A=4, B=3, C=2, which is the same order, > just shifted. Condorcet might have problems with completion rules when > there is a circular tie, but a Condorcet winner should be the same either > way. > > I'd try to figure it out, but I'm at work now. :D > > Michael Rouse > [EMAIL PROTECTED] > > > ---- > election-methods mailing list - see http://electorama.com/em for list info > ---- election-methods mailing list - see http://electorama.com/em for list info