Eliminating A doesn't mean not counting the A>B voters. Then it's B who is the only one who can win at Nash Equilibrium. B wins. NEO, too, fails CD. Evidently CD is incompatible with MAM strategy. Michael Ossipoff

Mike, You recently wrote: > Smith//MMPO has replaced Plain MMPO as an advocacy of mine. Do you still advocate Smith//MMPO ? It seems very similar to Winning Votes (MAM, Schulze, River, Smith//MinMax) except less decisive. 35 A>B 25 B 40 C B>C 60-40, C>A 40-35, A>B 35-25. MPO scores: C60 < A40 = B40. WV elects B, but MMPO gives an A=B tie. B winning fails CD and A winning fails Plurality. Also (like WV) it fails Mono-switch-plump. 25 A>B 26 B>C 23 C>A 22 C 04 A C>A 71-29, A>B 52-26, B>C 51-49. MPO scores: C51 < B52 < A71 MMPO and WV elect C, but if the 4A ballots change to 4C then they both elect B. 25 A>B 26 B>C 23 C>A 26 C C>A 75-26, A>B 48-26, B>C 51-49. MPO scores: B48 < C51 < A75. In my view C, being both positionally dominant and uncovered, is the prettiest winner. Chris Benham

On Sep 21, 2016 7:50 PM, "C.Benham" <cbenham@adam.com.au> wrote: > > > Mike, > > You recently wrote: >> >> Smith//MMPO has replaced Plain MMPO as an advocacy of mine. > > > Do you still advocate Smith//MMPO ? Yes I do. Though it doesn't meet CD, it meets Weak CD. Evidently MMC-like strategy is incompatible with CD. > > It seems very similar to Winning Votes (MAM, Schulze, River, Smith//MinMax)... Yes. If shares their optimally unproblematic strategy. You continued: ...except less decisive. (endquote) It can be decisive. If 2 candidates have the same max pairwise opposition, compare their next-largest pairwise opposition...& so on. You left out a property: Weak CD. > > 35 A>B > 25 B > 40 C > > B>C 60-40, C>A 40-35, A>B 35-25. MPO scores: C60 < A40 = B40. A wins. > WV elects B... ...rewarding defection. but MMPO gives an A=B tie. ...solved as described above. A wins You continue: B winning fails CD and A winning fails Plurality. (endquote) A is the most favorite candidate without majority pairwise opposition. If the Plurality Criterion says A shouldn't win, then the Plurality Criterion is mistaken. Plurality is a positional criterion. A positional standard won't give the desired properties. > Also (like WV) it fails Mono-switch-plump. That widely accepted, if wv does it. > 25 A>B > 26 B>C > 23 C>A > 22 C > 04 A > > C>A 71-29, A>B 52-26, B>C 51-49. MPO scores: C51 < B52 < A71 > > MMPO and WV elect C, but if the 4A ballots change to 4C then they both elect B. > > 25 A>B > 26 B>C > 23 C>A > 26 C Of course, as you know, rank methods have faults like that. Participation is another example. Avoid them with Approval. Michael Ossipoff > C>A 75-26, A>B 48-26, B>C 51-49. MPO scores: B48 < C51 < A75. > > In my view C, being both positionally dominant and uncovered, is the prettiest winner. > > Chris Benham >

Mike, 35 A>B 25 B 40 C > A is the most favorite candidate without majority pairwise opposition. C: Fortunately Smith//MMPO meets Irrelevant Ballots Independence, so let's make a slight change to the example so that there is no voted "majority" for anyone to fetishise about. 35 A>B 25 B 40 C 21 D Smith//MMPO still elects A. Your explanation to the C supporters as to why their favourite lost to A is now what? As is often the case with failures of the Plurality criterion, the the example is also an outrageous failure of Later-no-Help. If the A supporters had truncated like everyone else, then C would be the CW (and the only possible winner). Why should their ranking of B make their favourite (A) the winner? Especially since the method has some random-fill incentive, why should we assume that their ranking of B is sincere? What if their sincere preferences are just A or even A>C ? Part of your justification for Smith//MMPO is that it meets "Weak CD". But in a recent post on that criterion you wrote: > Not reassuring enough to be of much use. C: So I assumed that it was an idea you were just toying with before rejecting. > Evidently MAM -like strategy is incompatible with CD. C: What is "MAM-like strategy" and what do you think is so good ("optimally unproblematic") about it? > C: Also (like WV) it fails Mono-switch-plump. > > M: That's widely accepted, if wv does it. > IRV and Benham also fail the criterion, but they (unlike all the other proposed Condorcet methods I'm aware of) meet Unburiable Dominant Mutual Third (UDMT), which says that if the winner X is a member of a set S of candidates who are voted strictly above all outside-S candidates on more than a third of the ballots and who all pairwise beat all the outside-S candidates, then it isn't possible to cause the winner to change from X to some outside-S candidate Y by just altering some ballots that vote Y above X. So one of my current standards is that a method should meet at least one of Mono-switch-plump and UDMT. Is it one of your prejudices that anything that is "widely accepted", should be accepted? Chris Benham On 9/22/2016 11:05 PM, Michael Ossipoff wrote: > > > On Sep 21, 2016 7:50 PM, "C.Benham" <cbenham@adam.com.au > <mailto:cbenham@adam.com.au>> wrote: > > > > > > Mike, > > > > You recently wrote: > >> > >> Smith//MMPO has replaced Plain MMPO as an advocacy of mine. > > > > > > Do you still advocate Smith//MMPO ? > > Yes I do. Though it doesn't meet CD, it meets Weak CD. > > Evidently MAM -like strategy is incompatible with CD. > > > > It seems very similar to Winning Votes (MAM, Schulze, River, > Smith//MinMax)... > > Yes. If shares their optimally unproblematic strategy. > > You continued: > > ...except less decisive. > (endquote) > > It can be decisive. If 2 candidates have the same max pairwise > opposition, compare their next-largest pairwise opposition...& so on. > > You left out a property: Weak CD. > > > > > 35 A>B > > 25 B > > 40 C > > > > B>C 60-40, C>A 40-35, A>B 35-25. MPO scores: A40 = B40 < C60 > > A wins. > > > WV elects B... > > ...rewarding defection. > > but MMPO gives an A=B tie. > > ...solved as described above. A wins > > You continue: > > B winning fails CD and A winning fails Plurality. > > (endquote) > > A is the most favorite candidate without majority pairwise opposition. > > If the Plurality Criterion says A shouldn't win, then the Plurality > Criterion is mistaken. > > Plurality is a positional criterion. A positional standard won't give > the desired properties. > > > Also (like WV) it fails Mono-switch-plump. > > That widely accepted, if wv does it. > > > 25 A>B > > 26 B>C > > 23 C>A > > 22 C > > 04 A > > > > C>A 71-29, A>B 52-26, B>C 51-49. MPO scores: C51 < B52 < A71 > > > > MMPO and WV elect C, but if the 4A ballots change to 4C then > they both elect B. > > > > 25 A>B > > 26 B>C > > 23 C>A > > 26 C > > Of course, as you know, rank methods have faults like that. > Participation is another example. > > Avoid them with Approval. > > Michael Ossipoff > > > C>A 75-26, A>B 48-26, B>C 51-49. MPO scores: B48 < C51 < A75. > > > > In my view C, being both positionally dominant and uncovered, is the > prettiest winner. > > > > Chris Benham > > > > No virus found in this message. > Checked by AVG - www.avg.com <http://www.avg.com> > Version: 2016.0.7797 / Virus Database: 4656/13063 - Release Date: 09/22/16 >