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In April 2013 my attention was brought to a March 17, 2013 letter by
the Arizona League of Women Voters to a committee of the state's
senate.  The letter opposed allowing approval voting elections in cities
and towns in Arizona and stated that the League approved of ranked
choice voting, e.g., instant runoff voting (IRV) in single winner elections.
What was even more disturbing about the letter was that it was the
worst discourse I had ever read on voting systems in terms of dubious
and outright bogus claims.  As a result of my concerns, I wrote and sent
two e-mails, the texts of which are attached below in reverse order, to
two different representatives of the Arizona state chapter of the League.

The Arizona League isn't alone among League chapters in promoting
ranked choice elections, instant runoff voting in single winner elections.
For instance, at the time of this writing the Maine League of Women
Voters is on record as supporting ranked choice voting.  It also claims
that it has promoted political responsibility for over 90 years.  But it
is not doing so when it has on its website concerning ranked choice
voting statements about the advantages of ranked choice voting that
are patently inaccurate.

Some time after I encountered the Arizona League of Women Voters'
letter it became clear to me where the League got much of its
statement from:  FairVote's treatment of the issues concerning approval
voting and ranked choice voting, two systems which are discussed in
detail in the following appendix. 

From: John Howard Wilhelm
Date: Feb 17, 2014
Subject: AV and IRV a Follow-up
To: AZLWV Member No. 2

Madam,  If we want to improve our political processes in this
country, we clearly need to think carefully about reforming our
electoral system.  In doing so, we need to proceed from a respect
for facts, logic and evidence, not just simply from belief based on
hearsay and the like which too often has been the case for many
people regarding voting reform.  The 2010 referendum in California
that adopted the top-two runoff is an example of the latter with, as
the 2012 Egyptian presidential election shows, the potential for bad

In considering electoral or voting system reform, I am interested in
two important goals.  First, adopting a system that levels the voting
field for third parties.  And second, in using a voting system that also
does a good job in giving representative results of voters' preferences
in the outcome of single winner elections with three or more candidates.
For reasons set out in my April 25, 2013 e-mail attached below, instant
runoff or ranked choice voting does not meet these important criteria.

First, it is very clear from the Australian experience of 95 years with
the system,as well as experience in other places, that IRV does not
open up the political space to third parties.  If you look at Ka-Ping
Yee's simulations that William Poundstone has in his article "A Test
Drive of Voting Methods"

what stands out is the very great similarities of results between
plurality voting and IRV.  That is, both the empirical evidence and
the "theoretical" evidence strongly indicate that IRV will not do the
job of opening up elections to third parties.  Those who believe
otherwise need to demonstrate that the facts, logic of that voting
system and the evidence indicate otherwise.  In my reading of the
literature and the evidence, I have never found convincing material
to indicate otherwise.

Second, it is very clear that IRV as a voting system suffers from
serious defects that clearly significantly undermine its ability to
give representative results in terms of outcomes.  The most serious
of these that I focused on in my 2010 article on the Guardian's
"Comment is free" website and in my 2011 letter in the Financial
Times was the so-called monotonicity problem whereby getting
more support can harm a candidate and getting less can help a
candidate when IRV is used as an electoral system.

One response to my piece on the Guardian's website asserted
that the problem could occur only once in a hundred years.  But
there is clear evidence in 2009 that it occurred twice in this
country.  To date I have been able to determine that there were
a minimum of nine IRV election in that year in this country.  I
have no information on those other IRV elections and I doubt
anyone has since, unfortunately, in almost most cases the
information needed to determine this problem is not available in
the results released on such elections.  But, work done by a
number of mathematically competent people such as Professor
Norman, Warren Smith and Joe Ornstein indicate a troubling
rate.  And as far as I can determine, the more the candidates
the worse the problem.

From what I can see, the evidence indicates that this may well
occur one fifth of the time in close elections--surely very
troublesome.  How those associated with FairVote can ignore or
downplay this difficulty with IRV is beyond me.

Until our exchange I had never read of the later-no-harm criterion
in all of the large amount of literature I have seen on voting
systems.  This would seem to substantiate Warren Smith's
assertion that there is little about it in the literature.

From the Wikipedia entry, I understand that it strictly applies
to ranking voting systems which approval voting is not.  The
Wikipedia entry goes on to argue, though, that approval voting
can be interpreted as in fact violating that criterion.  But the
example the entry gives to demonstrate that is simply
implausible.  It assumes a simple case in which two thirds of
the voters (just two in the example) prefer candidate A and one
third (one voter) candidate B.  In the example the election
outcome is between only these two candidates.  But given
polls, I simply don't see in such situations that supporters
of A under approval voting would cast a vote for B and thus give
the election to B, which would be required to violate the
later-no-harm criterion according to the  Wikipedia's piece's

The only type of case under approval voting that I can see where
this example might work is the kind of situation in which you had
something like five candidates A through E where A and B are
reasonable people and C through E are really nasty people and
a voter under approval voting has no idea of the support level for
the candidates because of the absence of information on how
others are likely to vote.  Under such a situation it would be
rational to vote for both A and B although B may be viewed by
many as less desirable.  Formally, according to the Wikipedia
piece, this could be evidence of violation of the later-no-harm
criterion.  But that is surely inconsequential in such a situation.
In addition, approval voting is a transparent system and it
makes no pretense that in casting a vote for more than one
candidate that the voters are saying anything about their
preferences between the  candidates for whom they vote.

From what I understand, the later-no-harm criterion would be
violated in either a Condorcet election or a Borda election in
which candidates are ranked.  But once again, I don't see how
that is consequential.  The purpose of a Condorcet election is
to determine which candidate from a field in a multicandidate
election would win all the pairwise (one to one) elections possible
against all the others in such an election.  The classic Borda
election simply counts, as Dummett showed in his book
"Principles of Electoral Reform," the total number of votes each
candidate would get in all the pairwise elections possible from
the field of candidates with the candidate having the most total
votes being considered the most representative one.  I see no
way in, for instance, a sincere Condorcet or Borda election that
violation of the later-no-harm criterion would change those

In the literature the Condorcet leader or the Borda leader is
accepted as the most reasonable criteria for who among the
candidates in a single winner multicandidate election is the
most representative candidate.  If you look at Ka-Ping Yee's
simulations, it is clear that approval voting gives results quite
similar to those of Condorcet or Borda elections.  That is, it
does have a strong tendency to choose the most "representative"
candidate out of a field of candidates.

As far as I can determine, the later-no-harm criterion was
dredged up by people associated with the Center for Voting and
Democracy otherwise know as FairVote.  From my perspective
that is not a good sign.  Like its British cousin, FairVote is
largely a propaganda mill that seems to have minimal interest in
understanding the technical literature on voting systems or
promoting an impartial investigation of rival systems and the theory
of voting in general.

This may sound harsh, but let me give a concrete example of
that.  On its website Terry Bouricius is identified as "a senior
policy analyst for FairVote."  I have a piece which I understand
he wrote after the 2009 Burlington, VT IRV election.  In that
piece he states, "In terms of frequency of non-monotonicity in
real-world elections: there is no evidence that this has ever
played a role in any IRV election--not the IRV presidential
election in Ireland, nor the literally thousands of hotly contested
IRV federal elections that have taken place for generations in
Australia, or in any  of the IRV elections in the United States.

The latter part of the statement is patently untrue, the evidence
is that we had at least two non-monotonic IRV elections in
the U.S. in 2009.  The statement about Australian elections is
grossly misleading.  With perhaps one exception that I am aware
of, the Australians usually do not release the data to verify
monotonicity or non-monotonicity in their elections, so we simply
don't know and cannot make the statement that Bouricius did.
But I do know from Professor Norman that Australia has a lot
of close elections under his definition which would lead one to
suspect that non-monotonicity is a serious problem in too many
of their elections.

It is important to understand why this is a serious matter.  When
an election goes "topsy-turvy" in this manner it means that a
voter's vote does not have its intended consequence of helping or
hindering a particular candidate.

The same thing occurs in close elections with vote stealing.  The
only difference is the causal factor: a flawed voting system versus
a flawed conduct of the vote count.  For this reason and reasons
listed above in considering improving our voting system to get a
system fairer to both third parties and voters one needs to look
at other voting systems than IRV.

My electronic book at, especially my
first chapter and seventh appendix, sets out the case for
approval voting.  If that case is not convincingly made and it
is not based on facts, logic and evidence, I need to be told with
valid arguments, not just beliefs.  And I am willing to talk with
people about this which is why I hope that it will be possible to
engage you and your organization further on this.  Regards.

                                            John Howard Wilhelm
                                            Tel. 734/477-9942

From: John Howard Wilhelm
Date:  Apr 25, 2013
Subject: AV and IRV
To: AZLWV Member No. 1

Madam,  This past year and this year I have been trying to engage
the local chapters of the League of Women Voters in Minneapolis
and Ann Arbor, where I live, on the issue of voting reform to open up
our political processes to third parties.  As a result of a link Professor
Steven Brams of New York University sent me, I came across the
text of your organization's March 17 , 2013 letter to state legislators
which astonished me a great deal.  The person or persons who advised
you and your state chapter on the letter would appear from its text
to know very little about the technical literature on voting systems.

As a result of my concerns here, I called you League's office and
spoke with [a representative] who assured me that your state
organization is interested in exchanges on voting reform to open
up our political processes to third parties.  On this score, I would
like to bring your attention to my electronic book "Third Parties
and Voting Reform: The American Dilemma" on my website and to the attached PDF file of my
flier that I have been handing out on this issue.  In addition, I
would like to explain my position here with the hope you can
share it with your members.  But first I want to give you some
information on my background in this area to enable you to
judge my qualifications to address voting issues.

From September 1986 until I retired in July 2011, I worked as a
clerical assistant at Mathematical Reviews (MR) in Ann Arbor
which belongs to the American Mathematical Society.  MR
collects the world's serious mathematical literature to publish
reviews monthly on that literature for the world's mathematical
community.  As a result of materials we had, I came across and
acquired a copy of Brams' and Fishburn's book "Approval Voting."
It was of great interest to me because of my interest as a
specialist in reform in the former USSR.  And in fact in the
summer of 1991 in Moscow I gave a talk in Russian to a small
working group in the Soviet Academy of Sciences in which I
advocated using a variant of approval voting to elect a constituent
assembly to sort out the country's problems. 

After the 1992 election and Ross Perot's independent run for
office, I realized that approval voting had important relevance to
our situation.  As a result of my work at MR, I have acquired
more than a dozen serious books on voting systems and
numerous articles.  Over the years I wrote a number of pieces
which I edited into a twelve chapter electronic book to which
I have added appendices as I have learned more about voting
systems that challenged some of my previous assumptions.

In addition, over the years I have tried to work with members of
the Green Party, the Reform Party and most recently the
Modern Whig Party on the issue of voting reform.  Although I
am a nonmathematically  trained economist, I have now studied
and read an enormous volume of literature on voting systems and
believe that I have a very good understanding of this area with
respect to single-winner multicandidate elections.  I would like
to share some of my relevant observations in this area with you
in the hope that you can share it with your members as well.

In September 2010 the British Royal Statistical Society published
in its popular statistical journal Significance an article by Gavin
Thompson of the House of Commons Library on the issue of the
alternative vote as the British call our IRV (or Rank Choice Voting).
The article pointed out something that most supporters of IRV
do not seem to realize; the system does nothing to break away
from a system of two party dominance.  Indeed as Thompson
pointed out although Britain uses first-past-the-post or plurality
voting, as we largely  do, and Australia uses IRV in single-winner
election, the dominance of the two major parties in their national
legislatures is virtually the same in both countries.  Indeed my
own examination of Australian elections have confirmed that IRV
does virtually nothing for promoting third party participation in its
national legislature.  That is Duverger's law does not apply just
to our system of plurality voting but also to IRV as well.  In other
words, IRV has done and will do nothing to remove our voting
system's considerable barrier to third party participation in a
national legislature such as Congress.

But there is an even more serious problem with IRV that I pointed
out in my Guardian piece in the UK in 2010 with a numerical
example contributed by Professor Robert Norman of Dartmouth
College.  And that is, that a shift in public opinion towards a
candidate can lead to that  candidate losing, and a shift in public
opinion away from a candidate can lead to that candidate winning!
One commentator on my article asserted that this possibility is
so rare that it would occur only once in a century.  The empirical
and theoretical evidence simply does not substantiate that.  I
know that in 2009 there were at least 9 IRV elections in the US.
Of these, two elections exhibited that problem.  We don't know
how many of the other IRV elections that year ran into the same
problem.  But work done by Professor Norman, which I am sure
he can share with you, has indicated that in close elections, which
he carefully defines, this problem can arise in one fifth of such
elections.  The upshot of this is that in casting a vote in a
competitive IRV election a voter cannot know for sure whether
that vote (e.g., for first place) will help or hinder a candidate he
or she wants to support.  Even under our plurality voting system
such a situation would not arise.

The section of the March 17 letter dealing with gaming the system
is so full of erroneous statements and misrepresentations that I
really don't know where to start other than to comment that the
person or persons who helped on it clearly are not aware of the
Gibbard-Satterthwaite theorem and its implications for strategic
or tactical voting in single-winner multicandidate elections.  No
voting system can avoid situations in which there are no incentives
to vote tactically.  Under some voting systems as I point out in my
Appendix 8 such tactical voting is clearly malevolent.  But as I
argue, contrary to the assertion in the March 17 letter's gaming
section, tactical voting under approval voting is surely largely

In fact I argue that a distinct advantage of approval voting is that
it allows voters to vote both sincerely and tactically at the same
time to better represent their preferences in affecting the outcome.
In the case of a 2000 Florida-type election, for example, many of
those voting for a Nader could also have given in an approval
voting election a vote to a Gore leading to an outcome that would
be more representative of the preferences of those voting in such
an election.  By the way, the assertion by IRV supporters that
IRV elections get rid of the spoiler effect is not correct.  The
2009 IRV election in Burlington, VT that I analyze in Appendices
4 and 8 is an example.  The Republican candidate who had no
chance of being elected clearly played a spoiler role just as Nader
did in the 2000 Florida election.

At the time the top-two runoff system passed in the June 2010
California referendum, I was appalled by the fact that a large
number of obviously bright people in Silicon Valley supported it.
It was clear that they did not know the technical literature on
voting systems.  Unfortunately the March 17 letter from your
organization to your legislative representatives reflected a
similar problem.  I would hope that you and your members might
take a look at my website, especially
at the Guardian article, at the link on the first page of my website
under "Problems with IRV..." to the first video, and to Appendices
4 and 8 of my electronic book.  And I would hope that after that
we might have some more exchanges on a really crucial issue.

                                       John Howard Wilhelm, Ph.D.,
                                       4 West Eden Court
                                       Ann Arbor, Michigan 48108
                                       Tel. 734/477-9942

P.S.  By the way Sir Michael Dummett's book "Principles of
Electoral Reform," Oxford University Press 1997 is a must
read for anyone wanting to understand IRV and voting reform.