[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'?

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