If there are just two categories left, and neither one has a majority, what does it mean to fold them into their nearest neighbor categories? ... fold them into each other, and admit a tie between two categories as the Majority Judgment? That's not the kind of tie we are equipped to deal with. An odd number of categories at the outset will always prevent a category tie, so for each candidate a definite MJ will always be produced. Then the only ties to worry about are ties between candidates, which can be resolved by the standard MJ tie breaking procedure (remove the current tied mj, one copy at a time at a time from each tied candidate's collection of judgments ... until the ties are resolved or shown to be absolute ties ... leaving only the empty set for the candidates' common judgment basis). To me this is a deal breaker ... we cannot go with six categories! Choose three, five, seven, or nine, depending on the context ... how many and what kind of candidates ... human or inanimate choices/alternatives ...what kind of voters, etc. FWS El sáb., 23 de oct. de 2021 10:58 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > This works for any number of categories ... kind of like a symmetrical > version of Borda ... except that the collapses are done independently > rather than in concert ... > > WHILE there remains more than one judgment category inhabited by ballot > judgments for X ... > IF one of the outer two categories has more than half of X's ballot > judgments ... > THEN .... fold all of the other categories into that one majority > category... > ELSE ... fold the two outer categories into their nearest neighbors... > END WHILE > > The sole remaining category has the MJ for X. > > Finally!! ...the simple version of MJ that works for any number of > judgment categories!!! > > If six is your favorite, no problem; we can do it! > > We could use MJ itself to find the best number (i.e. majority judgment > number) of slots for public political elections. > > STAR, ASM(Ted Stern's version), and Standard MJ all use six slots ... any > reasons to change to five or seven? > > FWS >

ASM could be modified to work with an odd number of slots. Preferred ranks A and B would get 2 points. Acceptable rank C would get 1 point. Compromise ranks D and F would get zero points. Additionally, rank F, as the lowest rank, would get no pairwise votes over any other rank. Seed the initial ordering by total points and then proceed with sorted margins based on points. This could be adapted to any odd number of slots. On Sat, Oct 23, 2021, 23:41 Forest Simmons <forest.simmons21@gmail.com> wrote: > If there are just two categories left, and neither one has a majority, > what does it mean to fold them into their nearest neighbor categories? ... > fold them into each other, and admit a tie between two categories as the > Majority Judgment? That's not the kind of tie we are equipped to deal with. > > An odd number of categories at the outset will always prevent a category > tie, so for each candidate a definite MJ will always be produced. > > Then the only ties to worry about are ties between candidates, which can > be resolved by the standard MJ tie breaking procedure (remove the current > tied mj, one copy at a time at a time from each tied candidate's collection > of judgments ... until the ties are resolved or shown to be absolute ties > ... leaving only the empty set for the candidates' common judgment basis). > > To me this is a deal breaker ... we cannot go with six categories! Choose > three, five, seven, or nine, depending on the context ... how many and what > kind of candidates ... human or inanimate choices/alternatives ...what kind > of voters, etc. > > FWS > > El sáb., 23 de oct. de 2021 10:58 p. m., Forest Simmons < > forest.simmons21@gmail.com> escribió: > >> This works for any number of categories ... kind of like a symmetrical >> version of Borda ... except that the collapses are done independently >> rather than in concert ... >> >> WHILE there remains more than one judgment category inhabited by ballot >> judgments for X ... >> IF one of the outer two categories has more than half of X's ballot >> judgments ... >> THEN .... fold all of the other categories into that one majority >> category... >> ELSE ... fold the two outer categories into their nearest neighbors... >> END WHILE >> >> The sole remaining category has the MJ for X. >> >> Finally!! ...the simple version of MJ that works for any number of >> judgment categories!!! >> >> If six is your favorite, no problem; we can do it! >> >> We could use MJ itself to find the best number (i.e. majority judgment >> number) of slots for public political elections. >> >> STAR, ASM(Ted Stern's version), and Standard MJ all use six slots ... any >> reasons to change to five or seven? >> >> FWS >> > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >