[EM] Does IRV elect "majority winners?"

[Markus Schulze]

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