From: Simmons, Forest <[EMAIL PROTECTED]> > This method makes use of ordinal information as well as approval information.
So each voter would rank the candidates and also select one candidate as the threshold between approved and unapproved ? All unranked candidates being unapproved. > >1. Eliminate each candidate X for which there is a candidate Y such that on >each of more than half of the ballots Y is approved and X is not. What about going direct to Condorcet here ? Eliminate any candidate who is not in the Smith (or Schwartz) set and then use random ballot. I guess the problem being that voters who are going to lose might be willing to force a tie which gives them a chance of getting their candidate elected even though it also gives a lower preference a chance of being elected. I am not sure your method is immune from this. > >2. Use random ballot among the remaining candidates to choose the winner. > >Note that if any candidate X is eliminated, then some candidate Y must have more >than fifty percent approval, which makes her invulnerable to elimination. > >This method satisfies Monotonicity, Clone Independence, Independence from Pareto >Dominated Alternatives, Strong Favorite Betrayal Criterion, etc. In fact, as >near as I can tell there is no incentive for any insincere order reversal or >collapse. > >Of course, Random Ballot without step 1 satisfies all of those criteria, too, >but it is a bit too promiscuous with the probability. Assuming the votes are: 45: A, B approved ( B>A>>C ) 40: C approved ( C>>A>B ) The remaining 15 voters are of the opinion A>C>B if they approve A only: C is eliminated ( 45+15 = 60 votes approve A and not C ) result is: A: 40+15 = 55% B: 45 = 45% C: elim = 0% OTOH, if they approve C (tactical voting) A,B are eliminated ( 55% approve C and none other) results is A: elim= 0% B: elim= 0% C: 100% ( only remaining ) It is not clear to me that a 55% chance of your favorite and 45% chance of your lowest choice is superior to a 100% chance of your middle choice. This means that depending on the 15 voters relative preference strengths, it might be in their interests to tactical vote and just approve C, even though they prefer A to C. If the ranked choice must be consistant with the approval choice, they could just vote C approved and C first choice as a pure tactical vote. >With this new method any united majority can eliminate any dangerous candidate >from consideration. This majority defense feature has a name, but I won't try >to remember what it is. ---- election-methods mailing list - see http://electorama.com/em for list info
