Chris, I like this generalization!
Forest ----- Original Message ----- From: "C.Benham" Date: Sunday, November 20, 2011 8:04 am Subject: MTA vs. MCA (was "An ABE solution") To: em , Forest W Simmons , MIKE OSSIPOFF , "Dr Douglas R. Woodall" > > Forest Simmons wrote (17 Nov 2011): > > MTA vs. MCA > > I like MTA better than MCA because in the case where they differ > (two or > more > candidates with majorities of top preferences) the MCA decision > is made > only by > the voters whose ballots already had the effect of getting the > ”finalists” into > the final round, while the MTA decision reaches for broader support. > Because of this, in MTA there is less incentive to top rate a > lesser > evil. If > you don’t believe the fake polls about how hot the lesser evil > is, you > can take > a wait and see attitude by voting her in the middle slot. If it > turns > out that > she did end up as a finalist (against the greater evil) then > your ballot > will > give her full support in the final round. > > > > I buy this. I agree that MTA is a bit better than MCA. Well done Mike. > > * Voters submit 3-slot ratings ballots, default rating is Bottom > signifying least > preferred and not approved. Top-rating signifies most preferred > and > approved. > Middle-rating also signifies approval. > > If any candidates are Top-rated on more than half the ballots, > elect the > one of > these with the most approval. > > Otherwise elect the most approved candidate.* > > A slight marketing problem could be that the difference between > this and MCA > (and also between those and a third possible similar method: the > TR > winner wins if > s/he has majority approval, otherwise the most approved > candidate wins) > could > to some members of the public appear to be quite arbitrary and > unimportant. > Also of course MTA is little bit more complex to count than MCA. > But on > the positive > side, it has just occurred to me that it would work better than > MCA > extended to using > 4-slot ballots (with as with 3 slots, any rating above the > bottom-most > slot is interpreted > as approval). > > I suppose by the same reasoning we could improve ER- > Bucklin(whole), > which has > been given the briefer and quite apt new name by Mike O. of > "ABucklin". > My stab at defining the so improved version: > > *Voters submit ranking ballots, equal-ranking and truncation > allowed. > Ranked (i.e.not > truncated) candidates are considered to be approved. > > Rankings are interpreted as ratings thus: candidates ranked > below no > others are in the top > ratings slot. Those with x candidates ranked above them are in > (x-1)th. > ratings slot from > the top. (So A=B>D is interpreted as A and B in top slot, second- > highest > slot empty, > D in third-highest slot). > > Say the ratings slots are labelled from highest (signifying most > preferred) down as alphabetical > grades A, B, C, D etc. > > If any candidates are graded A on more than half the ballots > then elect > the most approved one > of these. > > Otherwise if any candidates are graded A or B on more than half > the > ballots then elect the most > approved one of these. > > Otherwise if any candidates are graded A or B or C on more than > half the > ballots then elect the > most approved one of these. > > Continue in this vein considering the next lowest grade each > round until > there is a winner, or if > that fails then elect the most approved candidate.* > > I think IBIFA is still quite a lot better than any of these > methods, but > it is more complicated. > IBIFA has a less strong truncation incentive and the IBIFA > winner will > never be pairwise-beaten > by the winner of any of these methods. > > Chris Benham > > > > > > > > > ---- Election-Methods mailing list - see http://electorama.com/em for list info
