How can mutual majority say "nothing?" Only if no combination has a majority. But A is in the A>B, B>A, and new A's, so A is on 56 ballots, which is a majority of ballots (and no one else is)
If a majority of voters (with the new voters, and where did they come from anyway) the only candidate with a majority win is A. Using "Mutual majority says: When a majority of the voters strictly prefers every candidate of a given set of candidates to every candidate outside this set of candidates, then the winner must be chosen from this set of candidates." we get after adding five voters from theoretical space, only A meets this criterion. -----Original Message----- From: election-methods-boun...@lists.electorama.com [mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Markus Schulze Sent: Saturday, January 10, 2009 2:45 PM To: election-meth...@electorama.com Subject: Re: [EM] "Beatpath GMC" compliance a mistaken standard? Dear Paul Kislanko, Kevin Venzke wrote (10 Jan 2009): > [Situation #1] > > 26 A>B > 25 B>A > 49 C > > Mutual Majority elects {A,B} > > Now add 5 A bullet votes: > > [Situation #2] > > 26 A>B > 25 B>A > 49 C > 5 A > > Now Mutual Majority elects {A,B,C}. You wrote (10 Jan 2009): > I guess I don't understand "mutual majority", then, > because after adding 5 votes it takes 53 votes to > have a majority, and only A has a majority. B is > 51/105 and C is 45/105. > > Five bullet-votes for A appear to change (A,B) to (A). Mutual majority says: When a majority of the voters strictly prefers every candidate of a given set of candidates to every candidate outside this set of candidates, then the winner must be chosen from this set of candidates. column1 = set of candidates column2 = number of voters who strictly prefer every candidate in column1 to every candidate outside column1 ************ For situation #1, we get: column1 / column2 A / 26 B / 25 C / 49 AB / 51 AC / 0 BC / 0 So mutual majority says that the winner must be chosen from {A,B}. ************ For situation #2, we get: column1 / column2 A / 31 B / 25 C / 49 AB / 51 AC / 0 BC / 0 So mutual majority says nothing. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info