I have an idea for a new 3-slot voting method: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved).
Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their approval-opposition (AO) score. (X's AO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* This clearly meets Favourite Betrayal, Participation, mono-raise, mono-append, 3-slot Majority for Solid Coalitions, "Strong Minimal Denfense" (and so Minimal Defense and Woodall's Plurality criterion), Independence of Irrelevant Ballots. This "3-slot Strong Minimal Defense, Equal-Ranking First-Preference Plurality (Whole)" method is my new clear favourite 3-slot single-winner method. One small technical disadvantage it has compared to Majority Choice Approval (MCA) and ER-Bucklin(Whole) and maybe Kevin Venzke's ICA method is that it fails what I've been calling "Possible Approval Winner" (PAW). 35: A 10: A=B 30: B>C 25: C Approval scores: A45, B40, C55 Approval Opp.: A55, B35, C45 Top-ratings score: A45, B40, C25. C's approval opposition to A is 55, higher than A's approval score of 45, so A is disqualified. The undisqualified candidate with the highest top-ratings score is B, so B wins. But if we pretend that on each ballot there is an invisible approval threshold that makes some distinction among the candidates but not among those with the same rank, then B cannot have an approval score as high a A's. This example is from Kevin Venzke, which he gave to show that Schulze (also) elects B and so fails this criterion. It doesn't bother me very much. MCA and Bucklin elect C. It is more Condorcetish and has a less severe later-harm problem than MCA, Bucklin, or Cardinal Ratings (aka Range, Average Rating, etc.) 40: A>B 35: B 25: C Approval scores: A40, B75, C25 Approval Opp.: A35, B25, C75 Top-ratings scores: A40, B35, C25 They elect B, but SMD,FPP(w) elects the Condorcet winner A. It seems a bit less vulnerable to Burial strategy than Schulze. 46: A>B 44: B>C (sincere is B>A) 05: C>A 05: C>B Approval scores: A51, B95, C54 Approval Opp.: A49, B05, C46 Top-ratings scores: A46, B44, C10. In this admittedly not very realistic scenario, no candidate is disqualified and so A wins. Schulze elects the buriers' favourite B. Chris Benham Send instant messages to your online friends http://au.messenger.yahoo.com
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