James, I just don't think it is reasonable to call any method but plurality itself a "plurality method" or to dismiss approval voting as only marginally better than plurality.
I'm not a voting methods expert -- certainly much less so than you and many other participants on this list. I'm not even clear about the meaning of some of the terms you use, including "mutual majority criterion" and "minimal dominant set efficiency," which is why I can't address some of your arguments. Nevertheless, from everything I have read and figured out on my own, approval is far better then plurality for all voting situations (i.e., situations ranging from informal groups needing to make quick decisions to presidential elections), and in some situations (especially small informal groups needing to make quick decisions), approval is far and away the best method -- indeed, the only very good method that I'm aware of. Now if you and Steven Brams were to debate approval voting and you were to persuade all or most people attending the debate that he has been a fool for advocating it all these years, then I might change my mind. But I really doubt that you could do that. My guess is that if you tried in such a debate to argue that approval is only marginally better than plurality, Brams would prove that it is you, not he, who deserves to be called a fool. I don't think you are a fool, but I do think it would be foolish for you to continue treating approval voting as dismissively as you have been and insisting that it is only marginally better than plurality. Ultimately, whether or not approval or other methods are "majority" methods is a question of debatable definitions. If approval voting would result in a Condorcet winner 95% of the time (just a guess, of course), that would be sufficient for many people who are less perfectionistic than you to regard it as a majority method. Moreover, any process for making collective decisions, including plurality voting and even some random selection processes, could be considered a majority process if it were chosen by a majority of voters and they agreed beforehand to accept the outcome of the process. In fact, I believe there are many situations where voter approved random selection processes, especially ones modified to insure proportional representation by qualified people of major ethnic and other interest groups, would be preferable to elections, no matter what voting method were used. But that's a subject for another discussion. -Ralph --------------------------------------------------------- You wrote: Ralph, you objected to the term "pseudomajority methods" for non-majoritarian single-winner methods, on the grounds that it was too derogatory. So, how about "plurality methods" instead? This is appropriate for methods like approval, range, and Borda, because what matter is who has the highest cumulative score, rather than which candidates are preferred by a majority over which other candidates. In that case, I would update my single-winner classification system as follows: Criterion 1: If a majority of the electorate coordinates their efforts, they can assure that a given candidate is elected, or that another given candidate is not elected. Criterion 2: Mutual majority criterion Criterion 3: Condorcet efficiency Criterion 4: Minimal dominant set (Smith, GeTChA) efficiency Criterion 1 only: Plurality methods. Criteria 1 and 2 only: Weak majority rule methods / mutual majority methods. Criteria 1, 2, and 3: Intermediate majority rule methods / Condorcet methods Criteria 1, 2, 3, and 4: Strong majority rule methods / strong Condorcet methods / top cycle methods Plurality methods: Plurality, approval, range voting, Borda Mutual majority methods: single-winner STV Condorcet methods: Minimax (aka SD, PC, etc.), Nanson, Black, etc. Strong Condorcet methods: ranked pairs, beatpath, river, cardinal pairwise (assuming that a strong-majority base method is used) ---- Election-methods mailing list - see http://electorama.com/em for list info