--- On Sun, 11/1/09, Paul Kislanko <kisla...@airmail.net> wrote: > Arrrgggg. Explain, someone, anyone, how MM can change an (A > B) to an (A B C) > possible winner set by adding voters for A.
One way to say this is that since in the first example there was a set of voters (26 A>B, 25 B>A) that had a mutual majority opinion on candidate set {A, B} the winner must come from this set. In the second example there is no such majority set of voters that would prefer some set of candidates, so the criterion says nothing. There is thus no requirement not to allow C to win. There is also no requirement to allow C to win. Note also that set {A, B, C} refers to all candidates, i.e. {A, B, C, D, ... ,Z} (if there are more candidates than the three mentioned three). There are methods that meet mutual majority and are "not very good". A method that would elect a random candidate from the set of all candidates but limiting the choice using the mutual majority criterion would be problematic in in the way you mention. Bullet votes would add C to the set of potential winners. Typically methods that meet mutual majority have however also other rules (or algorithm) that would elect the "most sensible" candidate from the sets {A, B} and {A, B, C}. Mutual majority could be just one of the criteria that the method meets. The behaviour of the methods is also often "smooth" in the sense that if there is almost mutual majority then the method elects a candidate that is (almost) in the mutual majority candidate set. So, even if some criterion may not apply in some set of votes the criterion may still roughly point out the direction where the winner will be found. > 26 A>B > 25 B>A > 49 C > > Mutual Majority elects {A,B} > > Now add 5 A bullet votes: > > 26 A>B > 25 B>A > 49 C > 5 A > > Now Mutual Majority elects {A,B,C}. Here words "Now Mutual Majority elects {A,B,C}" are a bit confusing since mutual majority doesn't set any requirements on who should be elected (nor "elect" anyone). There also seems to be a hidden assumption that there are no other candidates than A, B and C. Maybe it would be clearer to just say that any candidate can be elected (A, B, C or any other). Juho P.S. Also my direct mail to you was returned back to me (and this happened also with Kristofer Munsterhjelm some time ago). > -----Original Message----- > From: election-methods-boun...@lists.electorama.com > [mailto:election-methods-boun...@lists.electorama.com] On > Behalf Of > Kristofer Munsterhjelm > Sent: Sunday, January 11, 2009 2:23 AM > To: election-meth...@electorama.com > Cc: 'Markus Schulze' > Subject: Re: [EM] "Beatpath GMC" compliance a > mistaken standard? > > Paul Kislanko wrote: > > This still makes no sense to me, since C has no more a > majority in case 2 > > than it had in case 1. > > > > If mutual majority selects (A B) in case 1 and (A B C) > in case 2, it makes > > no sense at all and should never be mentioned again. > > Mutual majority can still be useful. Let's make an > analogy to Condorcet. > The Condorcet criterion elects the CW if there is one. In > other words, > if there is a CW and that CW is candidate X, then the set > from which > Condorcet methods elect is { X }. If there is no CW, and > the candidates > for election are {A B C ... X }, then the set from which > Condorcet > methods elect is {A B C ... X }. > > Thus, Condorcet is useful when there is indeed a CW, but > does nothing > when there isn't. > > So it is with mutual majority as well. When there's a > set that a > majority ranks above all the others, then a method that > passes mutual > majority must elect from that set. When there is no such > set, the method > is free to pick any candidate yet still pass mutual > majority. > > In that light, mutual majority seems very reasonable > indeed: if there is > a set so that a majority prefers that set to all others > outside the set, > then a candidate within that set should be elected. > It's simply > "majority" transported to sets. > > (And on another note, sorry for not mailing you this > directly as well, > Paul, but airmail.net seems to think my ISP is a dirty > spammer.) > ---- > Election-Methods mailing list - see > http://electorama.com/em for list info > > > ---- > Election-Methods mailing list - see > http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info