In a recent EM post in another thread, I defined and recommended the "Strong Minimal Defense, Top Ratings" method (that I first proposed in 2008) as "the best of the methods that meet the Favourite Betrayal criterion, and also the best 3-slot ballot 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 maximum approval-opposition (MAO) score. (X's MAO 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.* I gather from one off-list response that this sentence of mine could have been more clear: 'Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less strong incentive to truncate..' I neglected to mention that I think it is desirable that after top-voting X, ranking Y below X (but above bottom) should be about equally likely to help X as to harm X. This implies that if one of the the two LNhs are failed, it is desirable that the other is also. MCA/Bucklin meets Later-no-Help while failing Later-no-Harm. The voters have a big incentive to truncate, and to equal-rank at the top, so with strategic voters it tends to look like plain Approval. In SMD,TR after top-rating X, middle-rating Y may harm X or may help X. As discussed in 2008, it fails Mono-add-Top (and so Participation). 8: C 3: F 2: X>F 2: Y>F 2: Z>F F wins after all other candidates are disqualified, but if 2 F>C ballots are added C wins. Of course it is far from uniquely bad in that respect. A big plus for it is that it is virtually alone in meeting my proposed "Unmanipulable Majority" strategy criterion: Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html In common with MCA it meets mono-raise (aka ordinary monotonicity) and a 3-slot ballot version of Majority for Solid Coaltions, which says that if majority of the voters rate a subset S of the candidates above all the outside-S candidates, the winner must come from S. >From the post that introduced SMD,TR: 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,TR elects the Condorcet winner A. Chris Benham __________________________________________________________________________________ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ ---- Election-Methods mailing list - see http://electorama.com/em for list info