[EM] Real IRV Election, Disputable Result

Jan Kok jan.kok.5y at gmail.com
Wed Mar 15 21:00:00 PST 2006

On 3/12/06, radio deli <radiodeli at adelphia.net> wrote:
> Dear Jan,
> I saw your post on the Elections Methods List.  As a Vermont legislator, we
> may have to decide the issue of IRV on a statewide basis.

Welcome, Jim!  Thank you for taking an interest in voting reform, and
in what this group has to say about it.

>  To be honest, I'm
> not very enthusiastic about IRV.  I would prefer to support the candidate
> (not plural) of my choice, and if a runoff must occur between candidates I
> didn't support, then make a new decision based on the contest at hand.
> What are the problems you see with IRV?  Could you explain them in a way
> that people without a statistics degree (like me) could comprehend?  I hope
> you have a chance to respond---you seem quite knowledgeable on the topic!

Let me summarize what I think your main choices are, and my personal
recommendations, and then get into details.

I. Do nothing.  Keep the system you have now.  (We call it "Plurality
voting", or sometimes First Past the Post, FPTP.)
II. Adopt Plurality with a separate runoff round if no candidate gets
a majority of votes in the first round.
III. Adopt IRV.
IV. Adopt some other voting method.

My recommendations:

I. (Do nothing, keep Plurality.)  Obviously the easiest choice, but I
don't recommend it.  Plurality voting has some serious problems.  If
you aren't familiar with them, I recommend reading the first section
("Problems with Plurality Voting") of my "Better Voting Methods"
article at www.votebuddy.org/votemeth.htm .

II. (Adopt Plurality with runoff.)  I think this is a BAD idea.  It
can be expensive, and is somewhat dangerous, in that it can sometimes
elect widely disliked candidates.  I discuss this in detail below.

III. (Adopt IRV.)  This is my second-best recommendation.  I present
some pros and cons of IRV below.

IV. (Adopt some other method.)  This is my best recommendation.  Here
are three methods that are practical and popular with many of the
people on the election-methods list:

* Approval Voting.  This is the simplest possible reform, and it is a
vast improvement over Plurality voting.  Simply remove the
no-overvoting rule from the present voting rules, and allow people to
vote for as many candidates for an office as they wish.  Voters who
are happy with the Democratic or Republican candidate will usually
just vote for that one candidate, but a Green voter, for example,
might vote for both the Green and the Democrat.  This method can be
handled by any existing voting equipment - no upgrades needed.  For
more info, visit www.ApprovalVoting.com and www.ApprovalVoting.org .

* Range or Score Voting.  Voters assign a score (in a range of, say, 0
to 10) to each candidate.  The candidate who gets the highest average
score wins.  This method can also be handled by any existing voting
equipment.  For more info, see
math.temple.edu/~wds/crv/RangeVoting.html .

* Condorcet or Instant Round Robin Voting.  Voters indicate their 1st
choice candidate, 2nd choice, etc. using the same kind of ballots as
IRV.  However, the counting is different.  Candidates are compared, a
pair at a time, to see which candidate is preferred over the other in
each pair.  If there is a candidate who beats all the other candidates
in the pairwise comparisons (a "beats-all" candidate, more formally
known as a Condorcet Winner, CW), then that candidate wins. 
Washington state representative Toby Nixon is leading an effort to
adopt this method in Washington.  For more info, see
http://groups.yahoo.com/group/condorcet/ .

V. I assume that you (Jim) are mainly interested in possible voting
reform in Vermont state-controlled general elections.  But, _please_
also give some thought to voting reform within your party.  The types
of voting methods you use in your candidate selection process affect
the quality of the candidates that are eventually nominated. 
Candidates are often chosen by straight Plurality voting, or by
Plurality with runoffs.  As I show in the first section below, this
can sometimes lead to "fanatical" or special-interest candidates being
chosen as the winner.  These are candidates who have enthusiastic
support of a substantial minority of the party members, but are
strongly disliked or hated by a majority.  I invite you to consider
whether some of our past presidential candidates may have been
fanatical or special-interest candidates, who were selected by
Plurality-based elections.  I suggest that it would be in the best
interests of each individual party, as well as in the interest of the
entire country, to implement better voting methods in parties'
candidate selection processes!

Range Voting and Approval Voting tend to choose as winners candidates
who have a broad base of support.  A party that uses such a better
voting methods would be able to choose candidates that enjoy broader
popularity both within and outside the party.  Those candidates could
raise more money and support from within the party, and attract more
votes from outside the party.  I'd appreciate it, Jim, if you could
spread this idea around within your party: IT IS IN YOUR PARTY'S BEST
INTEREST to use the best possible voting methods for choosing your

Ok, here are more details about topics mentioned above:


There are several ways to implement plurality voting with runoff, but
the simplest and most usual way to do that in general elections is to
hold a runoff between the top two vote-getters, if no one got a
majority of the votes in the first ballot.

There are two main problems with this voting method:

1.  It's hard to say how often a runoff would be needed - maybe 10% of
elections would need a runoff? - but when it happens, it is a hassle
for everyone.  The candidates have probably spent their last dimes
campaigning to try to win the first round.  The election department
has to come up with more money to hold the runoff election.  The
candidates are exhausted.  The voters are exhausted.  The turnout for
runoff elections is usually much lower than for the main election.

2.  When there are several candidates of roughly equal strength in a
Plurality election, some of the top vote-getters can be "fanatical" or
special-interest candidates.  Those candidates are the first choice of
a significant fraction of the voters, but are hated by the rest of the
voters.  Meanwhile, many of the other candidates may be reasonable,
moderate, and acceptable to a majority of the voters, but because
there are several of them, they "split the vote" of the majority of
voters, so each candidate gets only a small fraction of the votes. 
The result is that the fanatical candidates can rise to the top, and
advance to the runoff election (or win immediately, if there is no

Some examples where this actually happened are:

- The 2002 French presidential election, where the anti-Semitic
Jean-Marie Le Pen advanced to the runoff to face the unpopular
incumbent president Jacques Chirac.  (Look up "Le Pen" and follow the
related links at wikipedia.org for more details.)

- The 1991 Louisiana gubernatorial open primary, where former Ku Klux
Klan leader David Duke advanced to the runoff to face the corrupt
former governor Edwin Edwards (who is now serving 10 years in prison
for racketeering!).  (Look up "David Duke" at wikipedia.org for more

The Republican party took extraordinary measures to prevent a
"fanatical candidate" (as defined above) from advancing to a runoff in
this example:  The 1990 Louisiana state senate race open primary
involved David Duke running as a Republican (without the party's
endorsement), the Republican-endorsed Ben Bagert, and the Democrat J.
Bennett Johnson.  Duke was polling 30 to 40% but was not expected to
get more than 40% if he advanced to a runoff.  Bagert was polling a
distant third.  Rather than face the embarrassment of having Duke
representing the Republicans in a runoff election against Johnson, the
Republican Party withdrew funding of Bagert's campaign. This forced
Bagert to quit the race, and allowed Johnson to get a majority of
votes in the primary election.  Thus, Johnson won the senate race
without need for a runoff in the November general election. 
("Louisiana Republican Quits, Reducing Duke's Chances", Washington
Post, October 5, 1990, page A1)

Note that all of these races were Plurality with top-two runoff. 
Plurality with runoff lulls voters into a false sense of security. 
Voters tend to believe that they can freely vote for their true
favorite candidate, and if a runoff occurs, they will have the
pleasure of choosing between two good candidates (the two "most
popular").  But, the argument and examples above show that sometimes
one or both of the candidates advancing to the runoff can be
unpalatable to a majority of the voters.


To be fair, perhaps I should first mention a few _good_ things about IRV:

1.  It is "instant", meaning that voters need to vote only once.  No
separate runoff is necessary.  (Most other methods discussed on this
list are "instant" also, regardless of whether it says so in the name
of the method.)

2.  IRV (and most other methods) allow voters to express an opinion
about more than one candidate, if they wish.  With Plurality voting,
you can only vote for one candidate - that's it!  Some people
(apparently including you, Jim) don't _want_ to vote for or provide
preference information about more than one candidate.  That's fine...
you don't have to.  In IRV (and most other methods), you can just mark
your first choice and be done with it.  But some people do appreciate
the opportunity to indicate their opinions of more than one candidate.

3.  IRV _alleviates_ most of the problems with Plurality voting. 
Personally, I would rather vote with IRV than with Plurality in
important elections.  However, I think there are _many_ methods that
are much better than IRV in a number of ways.

4.  Since IRV (as it is usually described and implemented) allows for
potentially several runoffs, IRV is much less likely to choose a
fanatical or special-interest candidate as winner, compared with
Plurality with top-two runoff discussed above.  For example, if IRV
had been used in the 2002 French presidential election, the winner
would probably have been Lionel Jospin.  Jospin was a relatively
moderate, well-respected candidate, the incumbent prime minister.  He
came in a close third place in the first round election, less than
0.7% behind Le Pen, and well ahead of the fourth-place candidate.

(An important side note:  I looked at Vermont's IRV bill several years
ago, and as far as I could tell, it specified a non-standard form of
IRV.  If no candidate got a majority of the first-choice votes, then
all but the top two vote-getters would be immediately eliminated and
their ballots would be redistributed to the top two vote-getters. 
This form of IRV would generally produce the same results as Plurality
with top-two runoff.  Please, Jim, if Vermont enacts IRV, make sure
that candidates are (effectively) eliminated one at a time, NOT all
but the top two at once.  That will reduce the danger of having a
fanatical candidate win.)

OK, so what are some problems with IRV?

1.  IRV can elect what might informally be called a "wrong winner". 
By that, I mean that there may be another candidate (called the
Condorcet winner, CW, or "beats-all" winner) who could beat every
other candidate (including the IRV winner) in one-on-one contests. 
Here is an example:

41 Left>Middle
10 Middle>Left
10 Middle>Right
39 Right>Middle

(That means: 41 voters voted for Left as 1st choice, and Middle as 2nd
choice.  10 voters voted for Middle as 1st choice and Left as 2nd
choice.  Etc.  "Left", "Middle" and "Right" are just names I've chosen
to the candidates, to hint at how they might be positioned on an
ideological spectrum.  I could have used "A", "B" and "C", or "Green",
"Democrat", "Republican", etc.)

How does IRV choose the winner in this election?  Well, Middle has the
fewest first-choice votes - he was listed as first choice on 20
ballots.  So Middle is eliminated, and his ballots are redistributed
to the next choices shown on those ballots.  The result is that Left
has 51 ballots in her pile, and Right has 49 ballots.  Left has a
majority of the ballots, and Left wins.

"So, what's wrong with that?" you may ask.  Let's look at the
preferences of the voters, as expressed in the ballots.  20 voters
indicated they like Middle best.  39 voters prefer Middle over Left. 
So there are 20+39=59 voters who prefer Middle over Left, and only 41
voters who prefer Left over Middle.  If Right had not entered the
race, we might reasonably expect that Middle would beat Left, 59 to

(Note that voters also prefer Middle over Right, 61 to 39.  So Middle
is the "beats-all" winner.)

So, who should win that race, Left or Middle?  Some IRV advocates
would argue for Left.  Personally, I would prefer Middle (the
beats-all winner).

One argument that IRV supporters might use to justify Left as winner,
is that Left has stronger 1st-choice support.  My reply: 1. If
1st-choice support is the golden standard, why bother with IRV? 
Plurality is _guaranteed_ to choose the candidate with the most
1st-choice support!  2.  1st-choice support is actually not a very
good standard at all.  There is a danger that a fanatical or
special-interest candidate could end up with a plurality of votes and

Another argument justifying Left as winner is that Left is the
"majority winner" or is "supported by the majority".  (This argument
is usually used as a slogan to sell IRV to the general public.  I
wouldn't expect to hear it in a debate with advocates of other voting
methods.)  My reply: 1. The "majority" that IRV advocates refer to is
contrived.  The IRV winner is the candidate who ends up with a
majority of the ballots.  But is it fair to say that all the voters
whose ballots were transferred to Left actually "support" Left?  (For
example, if the 2004 presidential election had been held using IRV,
many people might have voted Cobb>Nader>Kerry.  Most of Cobb's and
Nader's ballots would have ended up on Kerry's pile.  But would the
people who voted Cobb>Nader>Kerry or Nader>Cobb>Kerry agree that they
"supported" Kerry?  I think some would disagree!)  2. There are lots
of ways to count the ballots, measure the "support" for various
candidates, and claim that a candidate has a "majority of support".  I
happen to find the type of "majority support" enjoyed by a beats-all
winner to be particularly convincing.  After all, the beats-all winner
is preferred by a majority of voters over EVERY other candidate!

I'll show one more example to show how IRV can choose a "wrong
winner", and then move on to some other problems with IRV.

17 FarLeft>Left>Middle
18 Left>Middle
32 Middle
17 Right>Middle
16 FarRight>Right>Middle

Middle seems like the logical choice to win, right?  But, let's see
who IRV chooses as winner...

FarRight is listed as 1st choice on the fewest ballots.  So FarRight
is eliminated, all of FarRight's ballots go to Right, and Right ends
up with 16+17=33 ballots.

Now FarLeft (among the surviving candidates) has the fewest ballots in
his pile.  So FarLeft is eliminated, all of FarLeft's ballots are
transferred to Left, and Left ends up with 17+18=35 ballots.

And now - surprise! - Middle has the fewest ballots in her pile, so
Middle is eliminated.  The Middle-first voters were apparently so
confident Middle would win that they didn't bother to indicate second
choices :-)  So those ballots are "exhausted"; they are ignored for
the remainder of the IRV counting.

In the final round, Left has 35 ballots in his pile, Right has 33, so Left wins.

In this example, Middle is the beats-all winner.  Looking at the
ballots, we see that voters prefer Middle over Left, 65 to 35.  They
prefer Middle over Right, 67 to 33.  Middle is preferred over FarLeft
and FarRight by even larger margins.

Both of the above examples illustrate a problem with IRV called the
"center squeeze" effect.  A centrist candidate can be "squeezed out"
by candidates on either side, even though the centrist candidate may
be preferred by a majority of voters to all other candidates.

2.  Another problem with IRV is that it can encourage strategic
voting, contrary to the claims of some IRV supporters.  Let's reuse
the first example to illustrate this.  Suppose voters vote their true
preferences, as follows:

41 Left>Middle
10 Middle>Left
10 Middle>Right
39 Right>Middle

Left wins, according to IRV.  That is the worst possible outcome, from
the point of view of the Right>Middle voters.  Can the Right>Middle
voters vote some other way, to get a better outcome?

Yes.  If at least 10 of the Right>Middle voters vote Middle>Right
instead, then the ballots will look like this:

41 Left>Middle
10 Middle>Left
20 Middle>Right
29 Right>Middle

In this case, Right is eliminated, the ballots go to Middle, and
Middle wins with 59 ballots.  From the viewpoint of the Right>Middle
voters, "Middle wins" is a better outcome than "Left wins".  Thus, if
polls show that people are expected to vote as in the first case (with
39 Right>Middle votes), then there will be an incentive for the
Right>Middle voters to vote Middle>Right instead; the Right>Middle
voters will feel a pressure to change their votes.

"What's wrong with that?" you may be wondering.  "Some voters can get
a better outcome by voting strategically, rather than sincerely.  If
they do that, the beats-all candidate wins, which Jan was saying is a
better outcome than having IRV choose a 'wrong winner'.  So where is
the problem??"

My replies:

a)  In situations such as the above, IRV pressures some voters to lie
about their preferences, and to "betray their favorite" candidate by
voting some other candidate higher than their favorite.  It puts the
voters into an uncomfortable spot.

Put yourself in the shoes of the Right>Middle voters in the above
axample.  Would you vote Right>Middle, and risk having your worst
nightmare (Left) win?  Or would you betray your favorite candidate
(Right) by voting Middle>Right, in order to try to help Middle win?

b)  When voters succumb to the pressure to vote strategically, the
voting results are not an accurate indication of voters' true
preferences.  Look at the last example above, where it shows 29
Right>Middle.  How could anyone tell that there are really 39 voters
who prefer Right>Middle?

Those inaccuracies can cause politicians and political analysts to
misestimate the amount of support for certain positions, if they base
their estimates on election results.  Also, if public campaign funds
are distributed in proportion to 1st-choice votes, then the inaccuracy
of the vote results causes the funds to be distributed unfairly. 
(Note: I do NOT support the idea of public campaign financing!  Don't
spend my tax money on candidates I don't like.  Let me spend my own
money as I see fit!)

3)  IRV _may_ require expensive upgrades to existing voting equipment
and software.  It depends on what equipment you have currently.  I
expect it takes a bit longer to fill out IRV ballots than Plurality
ballots, so more voting booths may be needed to keep voting lines from
getting long.  Finally, election staff and voters need to be educated
on the new voting method.  (Some of these expenses would be incurred
with other voting methods as well.  But Approval and Range Voting
don't need hardware or software upgrades.)

4)  With Plurality voting, it is common practice to post, at each
polling place, on the night of the election, a summary of the vote
results obtained at that polling place.  This allows interested
citizens to compare the results reported by the polling place election
judges with the results reported by the central election office, to
make sure election data doesn't get lost or altered between the
polling place and the election office.  This practice helps assure
election integrity.

Unfortunately, with IRV, the elections results obtained at the polling
places can't be concisely summarized, when there are more than about
three or four candidates in a race  Thus, it becomes impractical for
ordinary citizens to verify results obtained by the polling places
with the results as received by the elections office.  (Approval and
Range Voting elections can be concicely summarized.  Condorcet is not
so concisely summarizable as Approval and Range, but is better than

> Best Regards,
> Rep. Jim Condon
> Colchester, VT

Thanks again for your interest!  I hope this answer wasn't
overwhelming.  Please feel free to ask more questions.  I would
welcome any news you care to share with us about what is going on with
voting reform in Vermont.

- Jan

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