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'? I wrote (2 Jan 2009): > 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. You wrote (2 Jan 2009): > Markus, I don't know where the statement "the > winner always wins a majority of the votes" came > from, but it is not mine, and in my opinion, it > does not take the discussion any further forward.. > > What I wrote, very specifically, was "with the > requirement that to win, a candidate must obtain > a majority of the votes." Statements of this kind, > and in these words (or words almost identical > to these), are used when elections are held at > meetings and are conducted either by show of > hands or by informal paper ballot This form of > words distinguishes such elections from those > where a single-round plurality result would be > accepted, when the corresponding statement from > the Returning Officer would be something like > "and the winner will be the candidate with the > most votes". > > This thread is about the meaning of the > expression "a majority of the votes". > I presented the simple scenario above to see > what views there might be about the meaning of > "a majority of the votes" in that specific > situation. This thread is rather about the meaning of the expression "to win a majority of the votes". Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info