[EM] Does IRV elect "majority winners?"

Juho Laatu juho4880 at yahoo.co.uk
Mon Jan 5 15:52:00 PST 2009

--- On Tue, 6/1/09, James Gilmour <jgilmour at globalnet.co.uk> wrote:

> > 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?

The biggest difference is maybe that in
the latter case some of the D supporters
whose vote was non-transferable maybe
thought that D would survive longer in
the election and thereby they now regret
not ranking also other candidates.

>From the voting method calculation
process point of view it may however
make sense to say that those voters
considered the other candidates to be
equally good. From this point of view
their opinion was not ignored (or if
they think they were ignored that was
"their own fault").

It is just a matter of taste or matter
of definition if one calls this
decision a majority decision.

In the first example some of the D
supporters could have cast a blank
ballot on the second round. Would
this make a difference?

In any case all I expect here is a
clear definition of what one means
when one talks about majority. Is it
a majority of cast ballots, valid
ballots, citizens, eligible citizens,
votes that took position on this
pairwise comparison, ballots that
answered this question (there could
be many on a single ballot),...

In IRV one should of course also
clearly state what kind of a majority
(or non-majority) decision this is.
It was maybe "a majority decision
between the last remaining candidates".
This is at least one nice way to hide
the fact that some of the already
eliminated candidates could have been
a stronger "majority favourite" in
some way (e.g. a Condorcet winner).


> James
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