[EM] Does IRV elect "majority winners?"

Paul Kislanko kislanko at airmail.net
Fri Jan 2 13:11:06 PST 2009

I don't believe RRs or practical implementations thereof define percentages
this way.

For instance, the US Senate rules call for 60 votes, not 60% of the Senators
who vote, in their rules. Likewise by leaving the state, for a time Texas
Democrats delayed the (ridiculous) re-districting plan the Republicans
eventually got passed anyway by just reducing the numerator for a fixed

Legislatures who follow RRoO pretty much define majority by "majority of
eligible voters." If we want to depend upon majority-criteria we need to
pick whether we mean majority of voters or majority of eligible voters. If
we chose the latter definition then NO method can make such a claim, unless
it has a specific method for dealing with non-voters.

If we chose the "majority of voters" approach, then Bucklin is an efficient
way to find all majorities that support any alternative. IRV is problematic,
because the method changes the definition of "voters" in each round. I'm not
sure IRV is unconstitutional, but it is repugnant.

-----Original Message-----
From: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Terry
Sent: Friday, January 02, 2009 2:54 PM
To: jgilmour at globalnet.co.uk; election-methods at lists.electorama.com; Abd
ul-Rahman Lomax
Subject: Re: [EM] Does IRV elect "majority winners?"


I think you miss-understood James Gilmour's question. He was asking about 
an exhaustive ballot election without any ranked-choice ballots. In his 
scenario 100 voters vote in the first round and 92 vote in the second 
round. Does the final round winner with 47 votes win with "a majority?" 
Robert's Rules and governmental election statutes would describe this 
candidate as a majority winner I believe.

Terry Bouricius

----- Original Message ----- 
From: "Abd ul-Rahman Lomax" <abd at lomaxdesign.com>
To: <jgilmour at globalnet.co.uk>; <election-methods at lists.electorama.com>
Sent: Friday, January 02, 2009 3:23 PM
Subject: Re: [EM] Does IRV elect "majority winners?"

At 06:34 AM 1/2/2009, James Gilmour wrote:
>Dave Ketchum  > Sent: Friday, January 02, 2009 6:07 AM
> > Terry and Abd look set to duel forever.
> >
> > Conduct of elections is a serious topic, but both of them
> > offer too many words without usefully covering the topic.
>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
>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'?
>James Gilmour

How many people voted in the election? Looks to me like 100. Could be
more, actually; Robert's Rules considers all non-blank ballots that
might possibly intend a vote, including overvotes. But let's stick with 

How many people voted for A? We don't know, actually! IRV doesn't
count all the votes. However, what the method has found is 47. We
know that 47 voters voted for A.

Are the ballots with a single vote for D on them "votes"? Surely
those voters think they voted. Their ballots were recognized as legal.

The FairVote propaganda sometimes talks about "majority" without any
qualification at all as to what it refers to; they are depending on
voters imagining they know what it means, they know that this
imagination will lead them to support IRV. Sometimes, however, we
see, "majority of the votes." Or, in what is even more of a stretch,
"the winner will still be required to win a majority of the votes." A
requirement implies a standard that can fail. The IRV method can't
fail to find a "last round majority," it's simple math -- if we except 

But in Santa Clara, the arguments went further. "Majority of the
ballots" was used. Once again, one could weasel out of the claim of
deception. "Why, we just meant, of course, "majority of the ballots
containing a vote for a continuing candidate."

But any reasonable person, not knowing the details of IRV, would
interpret the words to be a general majority, a majority of all the votes 

What was found was a majority of unexhausted ballots found to contain
a vote for the IRV winner. Not a "majority of ballots," which implies
the general usage.

Further, these arguments are being made in a context where "majority"
has a very clear meaning, IRV is replacing, usually, top two runoff.
The primary *requires* a majority, a true majority, in order to
complete. When you tell these people that they can obtain a majority
without needing a runoff, they will very naturally assume that you
are talking about the *same thing.* The voters go to the polls and
cast their votes. Setting aside informal ballots, if more than half
of these voters support the winner, a majority has been found. The
details of the voting system are actually moot. Did a majority of the
voters who voted support the winner -- regardless of preference order?

A true majority is considered very desirable. IRV and Bucklin were
apparently replaced by top two runoff, at least in some places, and
the probable reason is that a majority was desired, and it was
realized that these methods don't accomplish that, unless you coerce
voters, as was tried in Oklahoma. (As is done in Australia.)

However, a more sensible approach would have been to use preferential
vote in the primary, thus avoiding *some* runoffs! I would argue that
Bucklin is better, because it doesn't suffer so badly from Center
Squeeze, and it probably provides sufficient LNH protection that
voters won't be significantly more reluctant to add additional
preferences than they are known to be with IRV. We saw very
significant usage of additional rankings in the municipal elections
where I've been able to find results.

As I've noted, those who support a frontrunner don't have much
incentive, with either method, to add ranks. With IRV, we don't know
from the standard reports, how much truncation is present among those
who vote for the top two.

Further, it seems to make a huge difference if the elections are
partisan or nonpartisan. In nonpartisan elections -- which is most of
the IRV implementations so far in the U.S. -- IRV functions almost
exactly like plurality, the first round winner goes on -- every
example so far at least before Nov 2008, which I haven't examined -- 
to win the election. In most elections, a majority is found in the
first round. Same as Plurality!

So, looking just at the runoffs, roughly nine of them, in no case was
there a "comeback election." In *real* runoffs, it seems to happen
about a third of the time, that the runner-up goes on to win the election.

Almost certainly, the runoffs were a truer indication of the
electorate's preferences, expecially if we consider preference
strength, than the IRV winner would be. I have some ideas as to why
IRV does simulate Plurality, it has to do with what motivates people
to vote as they do. But that vote transfers strongly tend to simply
maintain the lead of the first-round leader is known in Australia,
and those are partisan elections, where the comeback effect would be 

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