If I remember correctly Kevin Venzke's first post to this list was a geometric argument that the MMPO winner was apt to be closer to the voter median position in Approval than the Approval winner. The scenario he had in mind was something like this
Scenario One: 26 A 24 A=C 24 B=C 26 B The geometry was something like this: AAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBB _________________CCCCCCCCCCCCCCCCCCCCCCCC________________ It weemed pretty obvious that the MMPO winner C was more likely the true majority choice than than either of the tied approval winners A.or B. Not long after that Kevin came up with his MMPO bad example: Senario Two: 48 A 2 A=C 2 B=C 48 B. The MMPO winner C lacked too much approval to be the real winner. Kevin took back his proposal, and went on the bigger and better things like trying to convince Juho that MinMax (margins) was not an acceptable public proposal. either. But as I mentioned in a recent posting MMPO with symmetric completion is the same as MinMax(margins), and by exempting the top rank or slot from the symmetric completion, we get a really nice compromise between MMPO and MinMax(margins), and what's more this version gives the "right" answer in both scenarios above. Kevin was ever so close to proposing what I now call LRV "Least Resentment Voting" or more technically Bottom- Symmetric-Completion MMPO. In the first scenario above both A and B have max opposition of fifty, while the max opposition of C is 26 + 13 = 39, so C wins. In the second scenario, A and B still have max opposition of 50 each, but now C's max opposition is 48 + 24 = 72, so C loses, to a tie betwen A and B. Where is the cutoff where all three are tied? Scenario Three: 34 A 17 A=C 17 B=C 34 B In this scenario the max opposition (with the bottom symmetric completion rule in effect) is 34+17 for A, 34+17 for B, and 34 +17 for C. The second largest opposition to either A or B is 17+17=34, while the second largest opposition to C is still 34+17, so C loses the tied situation , and the winner is a toss up between A and B. ---- Election-Methods mailing list - see http://electorama.com/em for list info
