[EM] suggested improvement on Mutual Majority criterion/set (and MTA reviewd)
On 21 Dec 2011 I proposed this criterion: *The winner must come from the smallest set S of candidates about which the following is true: the number of ballots on which all the members (or sole member) is voted strictly above all the non-member candidates is greater than the number of ballots on which a (any) non-member candidate is voted strictly above all the members of S.* That is fairly clear, but the wording could perhaps be improved, say: *If the number of ballots on which some set S of candidates is voted strictly above all the candidates outside S is greater than the number of ballots on which all the members of S are voted below equal-top (i.e. strictly below some/any outside-S candidate), then the winner must come from S.* I tentatively suggested the name "Add-Top Proofed Solid Coalition Majority". A bit less clumsy would be "Add-Top Proofed Mutual Majority". Maybe there is a better name that either does without the word "Majority" or includes another word that qualifies it. For the time being I'll stick with Add-Top Proofed Mutual Majority (ATPMM) I gave this example: 45: A>B 20: A=B 32: B 03: D My criterion says that the winner must be A, but Mike Ossipoff's MTA method elects B. I did endorse MTA as an improvement on MCA, but since it (and not MCA) fails this (what I consider to be very important) criterion (and is also a bit more complicated than MCA) I now withdraw that endorsement. I still acknowledge that MTA may be a bit more "strategically comfortable" for voters, but I can't give that factor enough weight to make MTA acceptable or win its comparison with MCA. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] TTPBA//TR (a 3-slot ABE solution)
I have conferred off-list with Kevin Venzke, and now agree with him that the "Tied at Top Pairwise Disqualification, Top Ratings" method I suggested (20 Nov 2011) almost certainly does fail the FBC, so I withdraw that proposal and instead suggest this simpler method: *Voters submit 3-slot ratings ballots, default rating is Bottom signifying least preferred, Top rating signifies most preferred, the other ratings slot is Middle. According to the "Tied-at-the-Top" pairwise rule (TTP), candidate X beats candidate Y if the number of ballots on which X is given a higher rating than Y *plus the number of ballots on which X and Y are both rated Top* is greater than the number of ballots on which Y is given a higher rating than X. If any candidates (or candidate) TTP beats all other candidates, elect the one of these with the highest Top-Ratings (TR) score. Otherwise elect the candidate with the highest TR score.* I call this "Tied at Top rule Pairwise Beats-All// Top Ratings" (TTPBA//TR). It is similar to Kevin Venke's Improved Condorcet//Approval (ICA) method, the only difference being that it uses Top-Ratings instead of Approval. It was Kevin who invented the special "tied at the top" pairwise rule. http://wiki.electorama.com/wiki/index.php?title=Tied_at_the_top http://wiki.electorama.com/wiki/Improved_Condorcet_Approval http://nodesiege.tripod.com/elections/#methica TTPBA//TR (or TTBA,TR) meets the Plurality and Mono-add-Plump criteria. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MTA
I said that there's no justification to propose or use a method any more complicated than Approval, unless it avoids the co-operation/defection problem. MTA and MCA both elect B in the Approval bad-example. It seems to me that, due to some advantage, I decided that I'd vote by MCAOC voting instead of MTAOC voting in an Approval election among the 7 parties that I nominated. But, because I'd like to use more than 3 rank-positions, provided that AERLO is available, I'd use AOCBucklin instead of either in that election. Without AERLO, strategy becomes much less reliable and knowable with more than 3 slots. As I said, I'm not sure whether or not AERLO spoils FBC-compliance, but I nevertheless suggest having it as an option in the poll, and I will use it, if the poll happens. But, if AERLO spoils FBC-compliance, I wouldn't propose it publicly. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
