[EM] Does IRV elect "majority winners?"

James Gilmour jgilmour at globalnet.co.uk
Mon Jan 5 16:04:54 PST 2009

Juho Laatu  > Sent: Monday, January 05, 2009 10:46 PM
> One comment on concerns related to IRV's
> decision between the last two candidates
> on if that decision is a majority decision.
> Many ballots may have exhausted before the
> last round. As a result one may claim that
> the last round decision was not a majority
> decision.

Juho's post (rest cut) points to two quite separate issues:	
1. How is the 'winner decision' made in an IRV election?	
2. What claims can be made for that winner?

In the discussion so far, these two separate issues have been muddled together, as they usually are in descriptions of IRV and
discussions about IRV.

It may come as a surprise to some (or all) that the Electoral Reform Society (founded 1884) had no rules for IRV (STV single winner)
elections until 1978, when under the supervision of Robert Newland (ERS Chairman and mathematician) and Major Frank Britton (ERS
Director of Elections), I codified a set of such rules for the Society.

The standard STV-PR rules all refer to the calculation of a quota, but do make provision for the election of one or more winners
without a quota if that becomes necessary.  But it really makes no sense at all to apply that approach to a single-winner STV
election, so in the 1978 IRV rules we made no reference to a quota.  Instead, the winner, at any stage, was to be determined by this
simple rule:	

"If the vote for any one candidate equals or exceeds the votes of all the other candidates combined, that candidate shall be
declared elected."	

The rules also make it clear that each voter has only one vote and the votes are transferred on a contingency basis in accordance
with the successive preferences marked on the relevant ballot papers  -  this being an STV election.

Here you will see there is no reference to "a quota", nor is there any reference to "a majority" of any kind.  Neither is relevant
to the determination of the winner of an IRV election.  You will find the same form of words today in the detailed rules for IRV
(called "Alternative Vote") on the ERS website:	
I commend the wording of those ERS rules to anyone who needs rules for an IRV election.

Quite separately from how the winner is defined in the detailed voting system rules, there is a question about what claims may be
made for the winner of an IRV election in terms of votes and voters.  And THIS is where the issue of "majority" comes in.

It is quite clear (and now agreed) that the winner (A) of the Exhaustive Ballot example had "a majority of the votes" at the second
round and so was the rightful winner of that Exhaustive Ballot.  But it would quite wrong to say that candidate A had the support of
the majority of those who had taken part in that election, because there were two rounds in that one election and some who voted in
the first round opted not to vote in the second round.

So here we have an important difference between "a majority of the votes" and "a majority of the voters".  But neither is (or should
be) of any relevance to the detailed voting system rules for an IRV election.


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