A large body of electoral reformers are committed to STV [the single transfer vote] as
a religious faith; the Electoral Reform Society, in particular, is not a neutral body
impartially investigating rival systems and the theory of voting in general, but an
organization devoted to disseminating propaganda for STV.-- Sir Michael Dummett,
"Principles of Electoral Reform," Oxford University Press, 2004 Reprint, pp. 90-91.

A large body of electoral reformers are committed to ranked-choice voting as a
religious faith, the UK's Electoral Reform Society and the American organization
FairVote in particular are not neutral bodies impartially investigating rival
systems and the theory of voting in general, but are organizations devoted to
disseminating propaganda for ranked-choice voting.-- A Contemporary Update.

Approval voting is a method of voting to elect single winners that has adherents
among some voting theorists, but is unworkable in contested elections in which
voters have a stake in the outcome. -- From the FairVote website on approval voting.

                                           The Monotonicity Issue

On June 22, 2010, the Guardian Newspaper's website "Comment is free" published
my op-ed titled "Forget AV [the alternative vote--IRV in American parlance], we need
approval voting" with a subtitle that that "If the Lib Dems [in the UK] are serious
about electoral reform, they ought to consider the many flaws in the system [IRV] they
favor."  The op-ed, written with the help of Professor Robert Z. Norman of Dartmouth
College, contained a numerical example of a pathology that infests IRV (Instant Runoff
Voting) and STV, i.e., ranked-choice voting, but does not infest our systems of plurality
voting, Condorcet voting, Borda voting nor approval voting.

Under approval voting in single-winner multi-candidate elections voters are permitted
to give one vote each to the candidate or candidates they support with the candidate
having the most vote winning.  Under IRV in ranked-choice voting, voters are asked to
rank candidates in the order of their preferences.  If a candidate gets a majority of
first rank choices, he or she is automatically elected.  If not, the candidate with the
fewest  first place votes or rankings is dropped and his or hers voters' second place
choices are allocated to other candidates and another round is made to determine if
a candidate has a majority of the count.  If not, the process is repeated again until a
candidate emerges with a majority of the count and is declared the winner.

It is the process of dropping candidates and reallocating votes under IRV that gives
rise to its pathology.  Under IRV a candidate scheduled to win an election can wind
up losing  with  more support.  Conversely, a candidate scheduled to lose can wind
 up winning with less support.  This situation is known as violation of the
monotonicity criterion, the idea that more support should never disadvantage
a candidate and less support should never advantage a candidate.  Even our
system of plurality voting does not suffer this disadvantage despite its other
flaws.  A candidate set to win under a plurality election will always win when
he or she has more support and a candidate set to lose will always lose when he
or she has less support.  The opposite can occur under IRV because such shifts in
preferences change the order in which candidates are dropped and votes reallocated
in each stage of the runoff in instant runoff voting.  This clearly is a serious matter.
As Sir Michael Dummett put it in his book "Principles of Electoral Reform," "A voter
is entitled to be certain that, by ranking a candidate highest, he is not harming his
chances.  The fact that he cannot be certain of this under the alternative vote [our
IRV] is undoubtedly a grave defect of the system."  Dummett, p. 103.

How grave this defect is under IRV clearly depends on its frequency.  In response to
the numerical example of this in my June 22, 2010 op-ed one commenter wrote that
this is so rare that it would occur only once in a hundred years as is commonly believed
by a number of supporters of IRV.  Unfortunately, both the theoretical evidence and
empirical evidence do not support that conclusion.  In the United States in 2009 there
were two IRV elections, in Burlington, VT and Vail, CO in which nonmonotonicity
occurred.  To date I have been able to determine that there were a minimum of nine
IRV elections in that off election year.  In addition to the US cases there is an
indication that nonmonotonicity occurred in 2009 in Australia in a state by-election.
Such occurrences are simply too frequent  to be in a statistical sense examples of
"black swans."

It is very unlikely in the seven or so other 2009 IRV elections that anyone knows how
frequently additional monotonicity failures occurred simply for the fact that in
almost all IRV elections the data necessary to determine this are not released in
the results made public.  In a number of papers Joe Ornstein and Professor Norman
have done mathematical analysis of this issue in the case of competitive three
candidate IRV elections.  A competitive three IRV election is one in which none of the
three candidates in contention has more than 40% of the first place votes and none
has less than 25% of the first place votes.  A rough statement of their findings would
be that approximately one fifth, or 20%, of such elections exhibit monotonicity failures.

In response to Joseph Ornstein's and Robert Norman's paper on "Frequency of
monotonicity failure under Instant Runoff Voting: estimates based on a spacial model
of elections" in Public Choice (2014) 161: 1 - 9, one FairVote critic suggested that when
a monotonicity failure occurs it may be "undetected or even undetectable, given the
information about preference orderings available or divulged."  He then went on to
write that such a situation "is akin to the tree that falls in the forest where no one
hears it.  Ignorance is bliss."  In response to this, I would simply paraphrase a
statement I made in my April 28, 2011 letter in the Financial Times.  "You could achieve
the same results with our system of plurality voting by simply mandating vote stealing
in a fifth of the contests in such close elections you don't need to institute IRV to do
this, though that would clearly be the consequences of a yes vote on May 5, 2011 to
introduce IRV in British parliamentary elections."

The problem here is that monotonicity failures under IRV are part of a broader
phenomenon that affects the system,  its erratic behavior in determining an
outcome.  And that is its failure to meet the independence of irrelevant alternatives
criterion.  This criterion basically says that if in an election like the 2000 Florida
presidential election Gore is preferred to Bush introducing a Nader as a third
choice must not make Bush preferable to Gore.  In the case of ranked-choice voting
systems like IRV  or STV, small changes in preferences between minor candidates
can, by changing the order in which candidates are dropped and votes reallocated,
lead to dramatic changes in the outcomes.

Sir Michael Dummett illustrated this in his book "Principles of Electoral Reform"
very well; on this score it is useful to quote him on this in some detail.

     "[IRV] is erratic because, at later stages of the assessment process,
     it gives the same weight to some voters' second, third, or (when
     there are more than four candidates) fourth choices as it gives to
     other voters' first choices, while never giving any weight at all to
     some voters' second or later choices, according to the accident
     of which candidates are eliminated and in which order."  Dummett p. 105.

That is, the order in which candidates are eliminated under ranked-choice systems
can make a large difference to the outcomes, this is the source of their erratic

It goes without saying that the results in our system of plurality voting, in Condorcet
elections, in Borda elections or in approval voting elections are not impacted by such
shifts in preferences among minor candidates.  Nor are these systems, including
approval voting, subject to monotonicity failures.

                                                    Dubious Claims

In my April 28, 2011 Financial Times letter I made a statement about claims made
by supporters of IRV which is worthwhile quoting.

     "As Professor Steven Brams of New York University has pointed out there
     is a science of voting.  If you look at that literature, including your own
     Sir Michael Dummett's very fine book 'Principles of Electoral Reform"
     (Oxford University Press, 1997), it is very clear that claims as to the
     advantage of AV [our IRV] turn out on critical examination simply to be

Two examples of such bogus claims are the claims by IRV supporters that it will
move us away from the two-party duopoly engendered by our system of plurality
voting and that it will get rid of the spoiler role.

The argument that IRV will effectively open up our political processes to third
parties, e.g., the Green Party or the Libertarian Party, is simply belied by the
empirical and theoretical evidence.  As Gavin Thompson put it in the September
2010 issue of the popular statistical magazine "Significance" published by the
UK's Royal Statistical Society, "The Australian House of Representatives has
been elected using AV [the alternative vote or our IRV] since 1918.  Election
outcomes have proven only slightly more proportional than in the UK."  In the
UK, as in most American elections, plurality voting is used for parliamentary
elections, yet the proportions of two party dominance in the Australian House
of Representatives and the British House of Commons are virtually the same.

In 2009 when I looked at recent Australian data for its House of Representatives,
it was clear to me that IRV in Australia had done little to break with a two-party
duopoly.  According to a statement on the Center for Election Science's website,
"In the last three Australian (central government) House election cycles, zero
third-party members were elected in 2001.  Then zero in 2004. Then it happened
again in 2007 with the Nat Libs getting 65 and the Labor 83 seats with two seats
going to unaffiliated MPs."  Australia has a 150 member House of Representatives.

Some theoretical clues as to why this has been the case may be seen in simulations
by Ka-Ping Yee,  found in a piece by William Poundstone on his website titled "A
Test Drive of Voting Methods."  In it, Poundstone presents in graphical form the
results of simulations by Yee of sincere, as opposed to tactical, voting in plurality.
approval, Borda, Condorcet and IRV elections.  In Yee's simulations, the results of
plurality voting and IRV are similar to each other in contrast to the results of approval,
Borda and Condorcet which are also similar among themselves.  That is, in the
simulations  the IRV chart, with the exception of the monotonicity problem, often
looks like the plurality chart.

What the similarities between sincere plurality and sincere IRV appear to reflect
is what has been labeled the "center squeeze effect."  Under both sincere plurality
voting and sincere IRV voting there is a tendency for each system to shut the
"representative" candidate, or perhaps candidates, out of the race due to vote
splitting  from two sides.  It is vote splitting in general in plurality races that
Duverger cites in his well known law which suggests why plurality voting leads to
two party dominance.  All of this may well explain in large part why in the
Australian case IRV does not break with two-party duopoly as also appears to be
the case, as the voting specialist Warren Smith has pointed out, in other countries
using IRV.

In an article in the Spring/Summer issue of the "Green Horizon Magazine" Rob
Richie, the Executive Director of FairVote, stated that "Add in ranked-choice voting,
and we can kiss the "spoiler" argument goodbye and allow people to always vote
for whom they really want without argument."  p. 30.  Since IRV is the ranked-choice
system used for single winner elections, this implies that IRV gets rid of the spoiler
role and that voters under that system don't have to be concerned about a "wasted

If a candidate y would win an election and a candidate x enters the election and
neither y nor x wins, x is a spoiler.  The classical example of a spoiler is, of course,
Ralph Nader in the 2000 Florida presidential election.  It is true that had that election
been held under IRV, Gore would have won which does illustrate that IRV can mitigate
the spoiler role, a clear advantage that it has over our system of plurality voting in
that type of situation.  Gore would have won because under IRV when the third place
Nader was dropped many of his voters' second choice votes would have been
overwhelmingly for Gore over Bush.  Of course, in an approval voting election one
surely would have had the same results because many Nader supporters seeing
he had no chance could cast an additional vote for Gore.

But IRV does not fully "kiss the 'spoiler' argument goodbye."  The 2009 IRV Burlington, VT
election is an example.  In data from that election it is clear that the Republican candidate
played the role of a spoiler.  Had he not been in the election the data clearly show that
the Democrat candidate would have won over the Progressive candidate by over twice
the margin that the Progressive won by in that 2009 IRV election.  With the Republican
in the race neither he nor the Democratic candidate won which is a clear sign that by
voting for the Republican in the first place on the IRV ballot in the election, Republicans
in fact, like Nader voters in the 2000 Florida election, assured that their least favorite
candidate won.  That situation in a subsequent similar IRV election would surely
have enticed  more Republicans to list the Democrat first so as  not to "waste" their
first place vote.  Of course, under approval voting they could have shown their support
for the Republican while casting a second vote for the Democrat to assure that their
least favored candidate, the Progressive, did not win.  That is why one can make a
strong case that approval voting does get rid of the "wasted vote" problem whereas
IRV does not.

Given the erratic behavior of IRV, it is quite clear that under that system a minor
candidate could easily play a spoiler role, which, unlike  the situation of a Ralph
Nader in the 2000 Florida election, the system could not correct.  But because of
IRV's opacity as a voting system, this is not so obvious.  That is why proponents
of IRV can get by with making erroneous claims about IRV avoiding spoiler roles.
In the case of approval voting, the entrance of a minor candidate would not in of
itself result in a spoiler role because giving that candidate alone a vote would not
deny another candidate a vote.

In approval voting it always pays to vote for your most preferred candidate or
candidates.  That is, voters under approval voting, in contrast to plurality voting,
always gain and never lose by giving a vote to their favorite candidate or candidates.
Contrary to what supporters of IRV seem to believe, in deciding on whom to rank in
first place voters in situations like the 2009 Burlington, VT IRV election can face the
dilemma of ranking their first choice either sincerely or tactically.  Other claims for
IRV and critiques of approval voting on the part of IRV supporters are also too often
based on dubious arguments or patently false statements.

                                   Other Dubious or False Statements

The assertion that approval voting degenerates into plurality voting is an example
of this.  This has been labeled the "Burr Dilemma" flaw in approval voting.  This
"dilemma" can best be explained by an example Duverger used in explaining why
plurality voting leads to strong two-party dominance.  In his example , let us say
of a mayoral election in a French city with an electorate of 100,000, Duverger posited
that 40,000 of the electorate were Communists and 60,000 moderates.  In a plurality
election in which a voter can only give a vote to one candidate with the candidate
with the most votes, not necessarily a majority, winning, it is quite possible for a
candidate unacceptable to the majority of voters to win.  For instance, if there were
one Communist candidate for mayor and two moderate candidates for mayor who
roughly equally shared moderate support, the Communist could easily win with
approximately 40,000 votes to approximately 30,000 each for the moderate
candidates due to vote splitting among the moderate electorate.

To get around this kind of situation in countries with plurality voting systems,
majorities such as the moderates in our example have an incentive to form a
structure, a party, with a system like primaries in the American political system
for putting forward a single candidate.  To compete with this and avoid
dysfunctional vote splitting on their part, the others have an incentive to do the
same.  Once that is in place there are strong incentives on the part of voters to
work politically within these structures and to avoid wasting one's vote by voting
for a third party or independent candidate and avoid spoilers.  Hence our two-
party system.

Advocates of approval voting would point out that the institution of approval
voting is an alternative means of avoiding  the election of a candidate who is
unacceptable to the majority of voters.  The IRV opponents of approval voting
argue based on the Burr Dilemma in our example of the French mayoral election
that approval voting would degenerate into bullet voting for each of the moderates
in our example as each of the moderates try to undermine the other moderate
to win.  If it did so degenerate, we could easily wind up in our French mayoral
example with approximately 40,000 bullet votes for the Communist and
approximately 30,000 bullet votes apiece for the moderate candidates, in
other words the same as the plurality results.

There are compelling reasons for believing that this would be highly unlikely in
real world approval voting elections.  First,  as opposed to plurality voting, and
the other voting systems we have mentioned, approval voting is the only one that
allows voters to give votes to any top candidates whom they view as equally
preferable to all the rest.  There surely are situations under approval voting where
such voters can sincerely vote accordingly rather than to have to toss a coin to
decide whom to vote for as they would have to do under plurality voting because
in that system a voter is allowed only one vote.  Second, in situations like those
Nader voters encountered where their top choice has no chance of winning, they
still have the option under approval voting  to give a vote or votes to those among
likely winners whom they would rather see win rather than their credible opponents.
And third, as opposed to plurality voting where voters are confronted with voting
either sincerely, e.g., for a Nader, or strategically, e.g., for a Gore, voters under
approval voting can and more importantly clearly have an incentive to vote both
sincerely and, given the constraints of other voters' preferences, to vote strategically
as well to better reflect their preferences on the outcome of the election.

In the case of the 2009 Florida election had approval voting been in place the
results clearly would have been different from the actual plurality results in
that election because those who had voted for Gore not to waste their vote
could have also given a vote to their favorite Nader and those who voted for
Nader could have also given to vote to Gore with Gore surely the likely winner.
That's not degenerating into the actual plurality results in Florida in 2000.

While there have not been approval voting in political elections in the US there
have been in a number of professional societies with thousands of members
like the American Mathematical Society,  the Mathematical Association of
America and the American Psychological Association.  Some of the professional
approving elections have been studied and to my knowledge have not evidences
a Burr Dilemma phenomenon.
Proponents of IRV also tend to charge that approval voting is a voting system that
is most subject to tactical voting which they sometimes pejoratively label as
"gaming the system."   While they acknowledge that other voting systems are
subject to this in materials I have seen, they fail to explicitly point out that with
three or more candidates no voting system can be designed that avoids tactical
voting.  This is the well known Gibbard-Satterthwaite  theorem.  The proponents of
IRV also fail to point out, like too much of the technical literature on voting systems,
the difference between benevolent tactical voting and malevolent tactical voting
which could be labeled "gaming the system."

It would be my position that a distinct strength of approval voting is that it allows
voters to vote both sincerely and tactically at the same time as opposed to plurality
voting which all too often can presents voters with the option of either voting
sincerely or tactically.  Given the constraints of other voters' preferences on the
outcome of an election such flexibility allows voters to better express their
preferences in their voting to effect the outcome.  The result of the use of approval
voting in a 2000 type Florida election would be a clear example of beneficial tactical
voting in terms of getting a result that better reflects the preferences of those voters
whose votes counted in such elections.

The Borda system of voting is an example of a voting system that entails a malevolent
tactical voting effect. In a single-winner multi-candidate election using the Borda
system voters are asked to rank the candidates.  The candidate a voter ranks
first in a classical Borda election is assigned one point less than the number of
candidates.  The candidate a voter ranks second is assigned two points less than
the number of candidates.  And so it goes on to the candidate ranked last who
receives no points.

In a Borda election the scores each candidate gets from each voter's rankings are
summed over all the voters and the candidate with the highest score is the winner.
It turns out, as Sir Michael Dummett pointed out in his book "Principles of Electoral
Reform" that each candidate's Borda score represents the number of votes each
candidate would get in all the pair-wise, one-to-one, elections possible from the
field of candidates if each voter votes in those pair-wise elections consistent with
his or hers rankings of the candidates.

The problem with the Borda system is that it is very vulnerable to tactical voting in
that voters have a strong incentive to list last that candidate or candidates who
most threaten their first choice although they otherwise would rank such candidates
high.  The problem with such tactical voting under the Borda system, as many
anecdotal accounts indicate, is that it can often lead to a winner whom few of the
voters actually want or rank high.  That is, tactical voting under Borda can easily
lead to perverse results not unlike the monotonicity perversity.

Aside from something like the 2009 Burlington, VT IRV example cited above, IRV
as a voting system is on an individual basis largely resistant to tactical voting
because of its opacity and complexity as a voting system.  For instance, in a
field of five candidates the number of possible rankings of candidates is 120
(5! in mathematical notation).  To engage in any effective tactical voting under IRV
outside of something like the Burlington example an individual voter would have
to have a good idea of the likely frequencies of the 120 rankings, clearly a
daunting task.  But that has not prevented the widespread use in Australian
ranked-choice elections of How to Vote Cards passed out by political parties.
According to the results of one poll, at least half of Australian voters may use
such cards.  The problem with this is that rather than having in the election
process one voter's vote or ranking count with or against another's, you can have
one group of voters who engage in tactical voting determining which preferences
of other groups of voters are or are not taken into consideration in determining a
winner.  This surely is a perverse behavior that undermines the basic purpose
of having an election, which is to honestly consult all voters preferences to
determine what should be decided.

Tactical voting under approval voting is unlikely to involve misrepresenting one's
preferences leading to unintended outcomes.  If voters' first choice or choices
under approval voting have little chance of winning given the constraints of
other voters' preferences and those voters do have preferences among likely
winners, it surely is not insincere to cast a vote accordingly as a Nader's
supporters might have done in a 2000 Florida type approval voting election.
Nor does approval voting involve one group of voters determining which
preferences of other groups will or will not be fully expressed in tallying up
an election outcome as can occur under IRV,

A frequent critique by IRV opponents of approval voting is that it violates the
later-no-harm criterion which IRV does not with the clear implication that this is
a serious defect in any voting system where it occurs.  "The criterion is satisfied
in a voting system if a voter giving an additional ranking or positive rating to a
less-preferred candidate cannot cause a more preferred candidate to lose."
Formally this criterion applies to ranking systems, which approval voting is not
since there are no rankings in that system.  Those who charge that approval
voting violates the criterion argue in terms of a voter's subjective evaluation of
candidates to whom they give a vote which is not reflected in the vote itself
since all votes count equally under approval voting.

Approval voting is a very transparent system and it is certainly unclear why a
voter would knowingly give a vote to a subjectively lesser candidate and risk
causing a subjectively greater candidate to lose.  At the minimum a voter
would give a vote each to both candidates in such a situation which in itself
would not cause either candidate to lose, but could result in the greater
candidate not winning which he could have had the voter only cast a vote for
him.   In that situation it would be bizarre for a voter not to just give one vote
only to the greater candidate.

Under approval voting, because it doesn't involve a wasted vote, it always pays
for a voter to give a vote each to that candidate or candidates who have his
highest ranking.  Should the voter conclude that that candidate or those
candidates don't have a realistic chance of winning then he has to ask whether
he cares about the more realistic choices and if so for whom to cast an additional
vote along the same line, voting for the candidate or candidates he considers
to be in the second best category which could certainly entail more than just one
candidate.  In all of this, it is hard to see how any later-no-harm criterion is of any
real significance in approval voting although the situation described here involves
approval votes cast for subjectively greater and subjectively lesser candidates.

It is a significant fact that the Borda voting system does involve the later-no-harm
criterion and that is why it is so subject to tactical voting.  Under the Borda
system ranking an otherwise preferred second candidate in second place can
cause a first place candidate to lose which is why such candidates can wind up
actually being ranked lower.

The claim that IRV elections always leads to a majority candidate being elected
is as mirage as data from the 2009 Burlington, VT IRV mayoral election illustrates.
In that IRV election the Progressive candidate won by 4,314 votes to the
Republican's 4,064 votes or by a margin of 250 votes.  But the Progressive's vote
in the final round was less than half of the number of votes counted in the
penultimate round of the runoff which was 8833 of which half, or a majority, would
require a minimum of 4417 votes, not the 4,314 votes that the Progressive received
in the final round.  Worse yet, had the Democrat rather than the Republican gone
to the final runoff count, he would have won by 590 votes or a greater majority than
the actual majority of the vote count in the final round of the runoffs.  In that election
the Democrat was the Condorcet leader, that is the one candidate who in all the
pair-wise, one-to-one, elections from the field of candidates would have prevailed
against all the other candidates.  This illustrates the point that even in an Australian
type of IRV election in which voters must list preferences for all candidates, a
candidate with a lesser majority can win as compared to what another candidate
might have received had he been the winner's opponent in the final runoff.

On its website in discussing approval voting FairVote states that "With approval
voting...a candidate with the first choice support of more than 50% of voters can
lose to a candidate without a single first choice supporter."  Clearly this would
strike most readers as a serious problem, especially given that in this case it is
probably quite correct.  But is it really a serious problem if the desirable purpose
of a voting system is to elect in multi-candidate single-winner elections the most
"representative" candidate?  An answer to this can be conjectured by looking at
an election based on the following preference rankings by three groups consisting
of 29,000, 26,000 and 2,000 voters with the corresponding scores that the individual
candidates would get from each of the three rankings in a sincere Borda election.

          29,000                               26,000                               2,000

        A  87,000                           C  78,000                          D  6,000

        B  58,000                           B  52,000                          B  4,000

        C  29,000                           D  26,000                          C  2,000

        D     0                                A      0                              A     0


        A  87,000   B  114,000   C  109,000  D  32,000


        AB  29,000 to 28,000

        AC  29,000 to 28,000

        AD  29,000 to 28,000

In this situation A would be the clear winner in a plurality, IRV or Condorcet
election but not for a Borda election in which given his score, B, who is without
a single first choice supporter, is the winner with a score of 114,000 to A's
87,000.  In a situation like this in which you have a highly divisive candidate in
A's position, one surely could make an argument, as Dummett has for similar
situations, that B is a more representative candidate than A.  All of the voters
including A's supporters regard B to be the second best candidate and all but
A's supporters regard A as the worst.  In this case one can surely make a good
argument that B could clearly represent the opinion of all the voters in a
constituency better than A would.  Given this, a similar result under an approval
voting election surely would not be of serious concern and could well be an
appropriate outcome.

As an aside, it is interesting to note in our above example that if the 29,000 voters
decide to vote tactically by dropping B to last place in their rankings to try to
prevent B's wining in a Borda election, they would wind up electing C whom in
reality they value less than B.  This provides some clues as to why Borda elections
can give unrepresentative results when a significant number of voters engage in
tactical voting under the system.

In its text on approval voting FairVote states that approval voting "will face
significant political opposition due to violation of our common sense
understanding of majority rule." But as we argued above, a majority rule
candidate may not be the most representative candidate in an election. 
Nevertheless, given the transparency of the system as opposed to the
opacity of IRV in arriving at results, it is hard to see how voters would view the
results of an approval voting election as so undesirable in a majoritarian sense.
The purpose of an approval election is to elect the candidate approved by
the largest fraction of the electorate, which the system delivers.  From the
numbers in an approval voting election, it is easy to calculate and understand
the percentage approval level that the winning candidate has.  It is difficult to
see in general why voters would view say a 52% approval rate for an approval
vote winner that much different from a 52% winner in our plurality elections.
In the approval voting race that tells voters that the candidate who won had the
support of the largest fraction of the electorate which consists of 52% of the voters.
In an analogous plurality election the winner's 52% tells the electorate that the
winner had the support of 52% of those who voted.

                          Summary and Conclusion

At this point it's useful to turn to a summary and conclusion on the issues we
have been discussing in terms of approval voting and IRV as alternatives to our
current system of plurality voting.

In looking at the costs of elections it is true that IRV does avoid costs of runoffs
in an election system.  But so can approval voting.  However, an approval voting
reform is virtually costless since, as opposed to introducing IRV, it does not
require expenditures on new equipment and programming since it only entails a
change in the rules for voting and some additional counting to determine the
results.  In sum, an IRV election is not cheaper to run than an approval voting

As we have seen IRV on both theoretical and empirical grounds is not third party
friendly just as our current system of plurality voting is not.  Although approval
voting has not been tried in US competitive political elections, it is clear that it
levels the voting playing field for third parties and independent candidates because
of voters' ability to vote for such candidates without wasting their vote, or voice.

Whatever its weaknesses, approval voting is a transparent system that delivers
on a definite, and I would argue reasonable, criterion for selecting a winner in
multi-candidate elections.  Given its erratic nature, IRV does not exhibit any
reasonable criterion for selecting a winner due to the fact that small minor
changes in some voters' preferences can have disparate effects on the outcome.
This occurs because such minor changes have an impact on which candidates
are dropped and whose votes are reallocated in each level of the runoff necessary
to determine an outcome.  And this is the reason for IRV's violation of the
monotonicity criterion which, despite claims to the contrary. is a serious defect
of the system.

In short, approval voting gives better outcomes than IRV and approval voting
has the advantage of getting rid of the wasted vote and the spoiler role which
are major impediments to better elections and better governance in the US.