Steve, Kevin, Kristopher, anyone interested, Before joining discussion of the relative merits of MJ, IRV, MAM and similarly-motivated single-winner methods I confirm that I didn't invent MCA. Also it is very disappointing that the EM archive at Electorama appears to only go back to last year. Those three methods have very different criterion compliances. I (and Kevin and a few others) highly value the Favourite Betrayal criterion and MJ is the only one of these 3 to meet it. Another widely valued criterion compliance is Condorcet (unfortunately incompatible with Favourite Betrayal) and of these 3 that is only met by MAM. IRV is immune to Burial strategy and meets the "Chicken Dilemma" criterion (meaning that there isn't any "defection" incentive). Of these 3 methods IRV is the only one that is best of its type (based on the above mentioned criteria,IMHO) and (so) is the only one I like. I like its set of criterion-compliances except that I'm not a big fan of Later-no-Harm, because it encourages light-minded expression of weak preferences and makes it more likely that voters will go along with cynical preference-swap deals organised between parties/candidates. Fortunately IRV meets Later-no-Help (as does MJ). Without that IRV would have a random-fill incentive (which would be silly and bad for "Social Utility"). MJ is a version of Median Ratings with a tiebreaker that looks (to me) a bit awkward to handle and motivated by I'm-not-sure-what. I don't like Median Ratings because (a) it can fail to elect a candidate that is both the most Top-rated and the pairwise-beats-all winner (b) it has a very strong truncation incentive (i.e. for voters to only use the top and bottom grades) and (c) it fails the Irrelevant Ballots Independence criterion, that means that removing or adding a small number of ballots that make no preference-distinction among the competitive candidates can change the winner. Of the methods I prefer to MJ, the simplest and most similar is Majority Top Ratings. It uses a 3-slot ballot, default rating is bottom. If any candidate is rated top on more than half the ballots then the most top-rated candidate wins. Otherwise if more than one candidate is approved (i.e. rated above bottom) on more than half the ballots then the one of those that is most top rated wins. Otherwise the most approved candidate wins. (It was invented by Mike Ossipoff). So it is another version of Median Ratings. Like MJ it meets Favourite Betrayal and Later-no-Help and unfortunately also fails Irrelevant Ballots. I prefer it to MJ because it is much simpler and has a somewhat reduced truncation incentive. A method I vastly prefer to both of these also meets Favourite Betrayal, but meets Irrelevant Ballots and has much less truncation incentive (at the cost of strict compliance with Later-no-Help) and is much more likely to elect the Condorcet winner is "Irrelevant Ballots Independent Fall-back Approval" (IBIFA). *Voters fill in ratings ballots with as many slots as there are candidates up to say 4. Say A-B-C-D grading ballots are used. Default grade is D, meaning least preferred and not approved. Any other grade is interpreted as approval. If any candidate X is A-rated on more ballots than any other candidate is approved on ballots that don't A-rate X, then elect the most A-rated X. Otherwise if any candidate X is rated A or B on more ballots than any other candidate is approved on ballots that don't rate X A or B, elect the X that is most rated A or B. Otherwise elect the most approved candidate.* I invented this and first posted it on EM on 28/5/2010. I don't like MAM for various reasons and prefer several other Condorcet methods, but expanding on that can wait for another post. Chris Benham