Dear James Gilmour, you wrote (2 Jan 2009):
> So let's try a small number of numbers. > > At a meeting we need to elect one office-bearer > (single-office, single-winner). There are four > candidates and we decide to use the exhaustive > ballot (bottom elimination, one at a time) with > the requirement that to win, a candidate must > obtain a majority of the votes. > > First round votes: A 40; B 25; C 20; D 15. > No candidate has a majority, so we eliminate D. > > Second round votes: A 47; B 25; C 20. > It seems that some of those present who voted > for D in the first round did not want to vote in > the second round - but that is their privilege. > > QUESTION: did candidate A win at the second round > with 'a majority of the votes'? Whatever the statement "the winner always wins a majority of the votes" means, this statement must be defined in such a manner that you only need to know the winner for every possible situation (but you don't need to know the used algorithm to calculate the winner) to verify/falsify the validity of this statement. Otherwise, this statement is only a tautology. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info