[EM] Does IRV elect "majority winners?"

[James Gilmour]

> At 07:04 PM 1/2/2009, James Gilmour wrote:
> >So let's try again, with little bit of additional information that
> >was (more or less) implied first time.
> >
> >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.  East person is allowed to vote for only one candidate in 
> >each round of the exhaustive ballot and the votes for each
> >candidate are to be indicated by show of hands.
> > 
> >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'?


Answer  > Sent: Saturday, January 03, 2009 6:32 PM
> Yes, A won the second round with a majority of votes.

So we have made some progress.


Now let us suppose the meeting decides to hold this election by STV instead of by Exhaustive Ballot (STV = IRV in this single-winner
case).  Each person has only one vote and is required to show his or her contingency (STV!!) preferences for as many or as few
candidates as he or she wishes by writing the candidates' names in successive order down a small sheet of plain paper (top = 1 =
first preference).

When all the ballot papers have been collected up and the votes counted, we find:

First stage: first preferences: A 40;  B 25;  C 20;  D 15.
No candidate has a majority, so we eliminate D and transfer the votes that are transferable on D's 15 ballot papers.

Second stage: transfer of D's votes: A 7;  B 0;  C 0;  non-transferable 8. All 15 ballot papers accounted for.
Votes totals: A 47;  B 25;  C 20.

QUESTION: did candidate A win at the second stage with 'a majority of the votes'?

IF the answer to this question about the STV election is different from the answer above to the question about the Exhaustive
Ballot, why is it different?

James






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