[EM] Does IRV elect "majority winners?"

[James Gilmour]

> > James Gilmour  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'?

>Markus Schulze  >Sent: Friday, January 02, 2009 2:51 PM> 
> 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, 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.

James

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