At 01:23 PM 11/6/2008, Kathy Dopp wrote:
I posted three of these most recent affidavits of the defendants of
Instant Runoff Voting and STV here:
http://electionmathematics.org/em-IRV/DefendantsDocs/
The first two docs listed are by Fair Vote's new expert witness.
11AffidavitofDavidAusten-Smith.pdf
The summary of the paper, tells us right away what we are facing.
(hand copied from the PDF image.)
BACKGROUND
1. I am presently the Peter G. Peterson Professor of Corporate
Ethics at the Kellogg School of Management, Northwestern University.
My curriculum vitae is attached as Exhibit A. A true and correct
copy of my 1991 article, "Monotonicity in Electoral Systems" is
attached as Exhibit B.
INTRODUCTION
2. In paragraphs 4-8 of this affidavit, I explicitly address the
issue of the monotonicity of Instant Runoff Voting (IRV). Although
IRV is subject to the possibility of non-monotonicity, I argue that
this issue is largely irrelevant to the appeal of any given rule. In
particular, every reasonable voting rules suffers from the same
problem when there are at least three candidates for office.
3. In paragraphs 9-14 of this affidavit, I briefly review the import
of Arrow's Theorem, which demonstrates the impossibility of
identifying any wholly satisfactory voting rule for aggregating
individual preferences over more than two candidates. See Kenneth
Arrow, Social Choice and Individual Values, (1st ed., 1951); Kenneth
Arrow, Social Choice and Individual Values, (2nd ed., 1962).
Paragraph 1 gives us some useful background. The work he did, on
which he may be basing his present opinion, predates the widespread
realization, among election methods experts, that Arrow's theorem
does *not* state what he is claiming. Arrow, in particularly, set up
his definition of "voting rule" in such a way as to exclude, even
from consideration, rules which consider preference strength, which
allow the expression of equal preference, indeed, which take, as
input, anything other than a strict preference order, covering all
candidates. If there are three candidates, Arrow's Theorem, as
applied to practical voting systems (Arrow really wasn't writing
about voting systems, as such, but about deriving a social preference
order from the individual preference orders of the members of the
society) would require the voter to rank all three, without any
consideration of preference strength, so, for example, if the voter
ranks Abraham Lincoln, Martin Luther King, and Adolf Hitler, the
preference expressed for, say, Abraham Lincoln over Martin Luther
King, or vice-versa, is equal, as far as the system is concerned, to
the preference expressed for the least preferred of those two over
Adolf Hitler.
Arrow's theorem, likewise, would not apply to Top Two Runoff, a
system which IRV is replacing in Minneapolis. That is because a
necessary condition for Arrow's Theorem to apply is that a method be
deterministic, from a single collection of the preferences. Likewise,
Arrow's theorem doesn't cover Bucklin Voting, the system which was
outlawed in Minnesota by Brown v. Smallwood.
Thus, much of this paper is totally off the mark. But let's start
with monotonicity. This writer explicitly states that "every
reasonable voting rules suffers from the same problem." This is, in a
word, preposterous. It is quite possible to argue, as he does, that
the monotonicity problem is, in itself, of little practical import,
though the non-monotonicity of IRV is a symptom of the erratic
behavior of the method, something easily seen in Yee diagrams. Only
in a situation where there are two strong candidates, which
effectively converts IRV into a fancy version of Plurality, does the
behavior appear stable. However, to argue that every voting system is
non-monotonic is to make mincemeat of the concept. What has he done?
Was this a mere mistake in his first paragraph.
No. He's pulled a bait-and-switch. He shifts the definition of
"voting system." Arrow's theorem deals, as I mention above, with
deterministic systems only, and monotonicity failure in IRV takes
place in such a deterministic system. But in considering other voting
systems than IRV, he pulls in consideration of primary elections,
i.e., he is not considering the single elections using these other
rules, but some larger process. Yet the analysis of such
multiple-ballot systems, I'd bet dollars to donuts (I haven't read
the papers yet), will assume fixed preference, i.e., the runoff is
just an appendage to the primary, there is no new campaigning, no
shift in turnout, no opportunity for the voters to reconsider their votes.
Austen-Smith does precisely this in his analysis in paragraph 5. He
essentially claims that a primary/runoff system with majority rule
suffers from monotonicity failure, using the same example as used
with IRV. But this assumes fixed preferences, which is, in fact,
preposterous as to real elections. Further, the whole concept of
*seriousness* of monotonicity failure was impossible to examine under
the old paradigms, where election methods were judged according to
"election criteria" deemed "reasonable." "Seriousness" is something
that, to be anything other than purely subjective, requires
*measurement,* and only utility analysis can approach it.
If there is monotonicity failure resulting in the election of B
instead of A, but the voters who voted for A actually are *almost* as
satisfied with B, the failure isn't serious. On the other hand, if,
for these voters, the preference is strong, it is, for them at least,
a serious failure. And if we aggregate preference strength (Warren
Smith does this by aggregating "Bayesian Regret," a measure of how
much the election result deviates from the ideal result, as
considered by each voter), over all voters, we have an overall
measure of election quality.
IRV generally produces the same result as plurality, in nonpartisan
elections; current experience in the U.S. is proving this. (So far,
no counterexamples have appeared, in a substantial series of
elections.) (I.e., the first round leader wins, vote transfers if
more rounds are required do not shift the result.) However, when it
elects without having found a majority of ballots cast, it is easy to
show that it is almost certainly electing, in some cases, a candidate
who would be rejected by the electorate in a runoff. How serious a
problem this actually is would require study, and the data is not
being collected. However, that fact is simple to show: in real runoff
elections, as examined both by myself and by FairVote, there is a
"comeback election" in about one out of three runoffs. The leader in
the first round ended up losing the election, through an explicit vote.
IRV does *not* simulate top-two runoff, and Austen-Smith's argument
here is thoroughly defective, practically obtuse.
The baseline democratic process, majority rule, is far more
sophisticated, used as an election method, than is commonly
understood by election methods experts, because that field went
almost entirely toward consideration of single-ballot methods. Yet
Majority Rule, strictly speaking, is a two-candidate method. For
convenience, many ballots are collapsed into one, and that collapse
can cause some problems. But uncollapsed Majority Rule, where, for
example, an assembly might nominate A for an office and the question
is then presented, "Shall A be elected?" This is a two-candidate
election! The "candidates" are A and "no election." However, even
before the presentation of the question, any member of the assembly
could move to amend to substitute B for A. If the amendment passes,
clearly the electorate prefers B to A. This process, through a series
of votes, is, among other things, Condorcet compliant. That is, if
there is a single candidate preferred over every other candidate by a
majority of voters, this candidate will prevail.
Naturally, we don't do this for public elections. I'd argue that
there is a way that we could do it, and it would restore pure
democracy to public elections, but that is beyond the scope of this
comment. The point is that systems which allow, as a contingency when
there is majority failure, further polls, are generally more
sophisticated than analysis of the voting rule used in each stage
alone. *And that is with fixed preferences.* When preferences shift,
as they do in the real world in such processes, they reflect the
preferences of an electorate which has presumably become more
informed. Thus Robert's Rules of Order expresses a dislike of any
election method which is satisfied with less than a majority of
ballots cast for the winner, and, even where they suggest
preferential voting, giving an example that is, with the exception of
one detail, the same as "instant runoff voting," they insist on that
detail: if the vote transfers do not produce a majority of votes for
a candidate, the election must be repeated. They also dislike
eliminating candidates from the runoff, and the reason is that if you
do top-two elimination, you may eliminate a very good, compromise
candidate, i.e., even everyone's second choice, perhaps considered
almost as good, or even as good, as the best of the top two, *by
every voter.* (Remember, most voting methods do not allow the
expression of equal preference, except at the bottom. -- i.e., I
voted for Obama; I expressed equal preference for Nader and McCain,
because the voting system doesn't allow me to rank more deeply than
top preference.)
But Top-Two Runoff, supposedly, suffers from this problem, same as
IRV. Well, it might seem so, and it is so, if the runoff ballot is
restricted *and does not allow write-in candidates.* We are so
accustomed to situations where write-ins don't have a prayer that we
consider that taking a candidate off the ballot is the electoral
equivalent of shooting him. However, take this genuine compromise
winner off the ballot, and with an electorate that is at all awake
(and it only takes a few to make sufficient noise), that candidate
could win, even by a landslide, once it was made widely known that
there was a write-in campaign). I would have been skeptical about
this, myself, until I saw what happened in Long Beach, California,
where a mayor, excluded from the ballot by term limit rules, was the
plurality winner in a primary, and, with a runoff mandated and still
excluded from the runoff ballot, won (slightly short of a majority,
but plurality victory allowed in the runoff) the runoff. Long Beach
is a town of almost a half-million people. This was not some small,
quirky result. Write-in votes are a basic democratic right, and when
that is chipped away at, as it has been, democracy is the loser. In
San Francisco, write-ins used to be allowed in runoffs. There was one
runoff election held before IRV was implemented there, but write-ins
were not allowed. The rules were changed to prevent it; this was
challenged and was sustained by the California Supreme Court. The
decision turned on whether the primary and runoff were a single
election or two. The court decided as if it was a single election,
though, it is easy to show, it is two (different voters, in particular).
The first election determines two things: is there a candidate
supported by a majority? If so, that candidate is elected. If not,
the top two candidates -- as it's currently done, it *could* be done
much better -- are given ballot position in the runoff, and no other
candidates may be on that ballot. In San Francisco, though, they
could register as candidates and votes for them would be counted.
(San Francisco did not allow pure write-ins, but rather provided for
easy registration of candidates, which apparently was considered
adequate, and I'd agree.)
I'm not sure what the purpose of this affidavit is. Monotonicity
failure should not be an issue before the Minnesota Supreme Court,
except in one narrow way. The Brown v. Smallwood court discussed the
electoral situation in terms that indicated that they would be
displeased by a system whereby voting for your favorite could prevent
that candidate from winning. I can see that it might be useful to see
what arguments are being presented by the plaintiffs, here.
Monotonicity isn't what I'd focus on; rather, I'd be more concerned
about equal protection; IRV does not treat all *votes* equally.
Rather, votes are conditional or contingent in IRV. In real IRV
ballots, as being used in the U.S., only a limited number of
preferences may be expressed; you may vote, in San Francisco, for up
to three candidates. However, some elections have over twenty
candidates *on the ballot.* In Top-Two Runoff as they used to have --
and with so many candidates, majority failure was common, so runoffs
were common -- one could safely vote for one's favorite, period, and,
generally, the top two were simply the frontrunners from the start,
and then one could decide whether or not it was important to vote in
the runoff, where a clear choice was presented (and the voters could
look more deeply at each candidate, if they care.) (The effect of
preference strength on runoff elections is a seriously understudied
topic. It's been assumed that low runoff turnout is some sort of
problem, when, in fact it might be a good thing. It depends, and
without understanding preference strength, it's impossible to tell
the difference.)
Now, though, candidates are winning in San Francisco with less than a
majority of votes cast, as little as under forty percent. There are a
number of possible causes:
(1) Voters are voting sincerely, and sincerely prefer three
candidates on the ballot to either frontrunner.
(2) Voters are truncating their votes due to lack of sufficient
knowledge, perhaps. They know whom they want, so they vote for that
candidate, and leave it at that. A variation on this possibility is
that they detest all the candidates except, perhaps, the one they
voted for. (Note that sincerely voting for a write-in considered to
have no possibility of winning is actually a reasonable strategy in
Top-Two Runoff, if one thinks that this favorite candidate, not on
the ballot, might win a runoff. By casting a valid vote, one's vote
is included in the definition of "majority." Robert's Rules even
includes in the basis for majority, ballots with "No" written on
them, but not blank ballots. (The Libertarian concept of requiring
None of the Above on ballots is actually standard process under
Robert's Rules, i.e., in pure direct democracy.) Voting systems
theorists have, unfortunately, neglected these details, for obvious
reasons: it's messy. But that's reality.
In any case, if San Francisco wanted to stop paying for runoff
elections, they had a much simpler recourse than IRV, one which would
have produced quite the same election results: stop requiring a
majority. That is what they did, in fact, they just did it with a
fancy and expensive election system. If they wanted to continue to
require a majority (which I certainly recommend), there are much
better election methods than IRV. Bucklin, for example, which
Minnesota recommended, is far easier to count, and it is slightly
more efficient at finding majorities than IRV, because it counts,
when needed, all the votes. Bucklin deals quite well with the spoiler
effect. And it had long use in the United States. Why was it
rejected? I've seen no good account. In Minnesota, it was quite
popular, and the legal profession was generally perplexed -- or
offended -- by Brown v. Smallwood, read the decision and the dissent
and appeal for rehearing. It worked. In other states, where it was
used for primary elections, it's been claimed by FairVote that only
perhaps ten percent of voters were adding additional preferences, and
that they were not shifting results. But that's normal behavior.
*Note that this is what IRV is doing.* Results shift from the use of
preferential voting, for the most part, only in partisan elections,
where vote transfers exhibit consistent patterns; i.e., most
first-choice Nader votes would, when Nader is eliminated, go to Gore.
In spoiler elections, we see a few percent of votes, often less than
ten percent, which shift the result; one does not expect those who
sincerely favor Gore or Bush to cast additional votes; instead, only
those who favor a third party candidate would cast lower preference
votes for Gore or Bush.
(Again, in Brown v. Smallwood, though, we can see a possibly
nonpartisan election where the votes shifted the result, causing
Smallwood to win (in a clearly just result -- same as IRV would have
done --, overturned by the court, which makes me suspect partisan
bias; an unbiased court, finding a procedural problem in the method,
after the lapse of time involved, would have recognized that the
voters would be cheated by overturning the result, because they would
have voted differently if the method had been Plurality. So they
would have still outlawed Bucklin, but would have allowed the
election to stand, the "harm" done to Brown was .... well, this
reminds me of a recent U.S. Supreme Court case where "harm" was done
to a candidate or to those who voted for him, by his not being
promptly declared the winner pending clarification of the count.)
I would be very interested to know how Austen-Smith's 1991 paper was
received. It's old. I've already examined some of the underlying
assumptions; he builds a mathematical structure on them.
Now, as to Arrow's Theorem. In paragraph , after noting the
"hit-or-miss" approach of comparing election methods using
"reasonable" criteria, he claims that"
In 1951, Kenneth Arrow [...] proved a remarkable result: in effect,
there exists no unequivocally satisfactory, or normatively
appealing, voting rules.
This is good political spin. Without a qualifying "in effect," the
statement would be plain wrong. Arrow's Theorem isn't about "voting
rules." It is about something very narrow and specific, taking the
collection of individual "preference lists" -- strict, complete
preferences from members of a society, covering every possible choice
-- and aggregating them to a single "social preference order." He
showed that this process will necessarily violate one of a small set
of supposedly "reasonable" criteria. And there is no doubt about his
result, he proved what he proved.
But there are many "reasonable" voting systems which quite simply are
not covered by Arrow's Theorem. I've mentioned some exceptions above:
muliple-ballot systems, such as Top-Two runoff, or standard
majority-required elections (multiple ballots until you get a
majority) per Robert's Rules. Systems such as Approval Voting ask a
different question than "What is your preference order?" They ask,
instead, "What candidates would you accept?" or, probably more to the
point, "Which candidates, given practical realities as you see them,
are you willing to support." Take a method like this an add a
majority requirement, with a majority preference being necessary
(i.e., if two candidates get majority acceptance, there is, likewise,
a runoff), you've got an election method that isn't even contemplated
by Arrow's Theorem. Allow the expression of ratings, you have got a
method that, with sincere votes, produces a socially optimal outcome,
maximizing satisfaction with the result. The complaints about this
(this is Range Voting) are not based on violation of Arrow's
criteria. They are, instead, based on alleged strategic voting, i.e.,
that voters will warp the outcome, supposedly, by exaggerating their
votes. Again, this is not the place to argue what the best election
method is, but there is, in fact, a published paper that shows that
Range Voting is not only a counterexample to Arrow's Theorem (which
must be restated to even apply to Range Voting), but is a unique
solution. Unfortunately, the math is complex, and Warren Smith, a
mathematician, has criticized the authors for using "notation from hell."
Nevertheless, the point is that Arrow's Theorem doesn't apply, even,
to the system that IRV is replacing, Top Two Runoff. This is not to
say that TTR is perfect, it isn't.
What Austen-Smith has done, and he's not the first, is to confuse a
potential analytical technique (the translation of individual
preference orders, presumably sincere, into an overall social
preference order) with a political system, whereby a community makes
decisions. It turns out that Social Preference Order isn't even very
useful, because "order" neglects, entirely, preference strength. Far
more useful would be, for example, a knowledge of the actual impact
of each decision on each member of the society. Then, with some
system of making individual welfare commensurable across the society
-- not a simple problem, to be sure, but there are reasonable
approaches -- one can determine a measure of overall benefit or loss
from each possible decision. What the Range Voting people have done
is to call the Range Vote a "Voter Satisfaction" measure. I.e., when
you vote for a candidate, you are expressing your expected
satisfaction with the election result, with, say, 10 indicating
maximum satisfaction, and 0 indicating minimum. The expression for
each candidate is unconstrained by the expression for any other
candidate, but, of course, these are votes. It is as if, in such a
system, you are casting ten votes, or, a better analysis, fractions
of a vote, i.e., for each candidate, you are casting a vote in the
range of 0 to 1. Thus, Approval Voting is a limiting case, it is
simply Range Voting with only two possible "ratings."
Right away those who have been accustomed to using "election
criteria" to judge election methods, when Brams proposed Approval
Voting as a "strategy-free voting method," noticed that the sacred
cow, the Majority Criterion, was apparently violated by Approval
Voting. This was often translated into violation of "Majority Rule,"
FairVote propaganda does that, in criticizing Approval. But "Majority
Rule," as I noted above, involves a bivalued choice. Approval
violations of the Majority Criterion, allegedly -- there are problems
involved in the definition of the Majority Criterion -- involve a
situation where more than one candidate has been approved by a
majority. If that's considered a problem (it's debatable), it's easy
to fix, in a manner that would cover nearly every real situation: a
runoff. But in real political elections, multiple majorities can be
expected to be extraordinarily rare. As I've written, we should be so
lucky. In U.S. Presidential 2000, for example, if the method in
Florida had been Approval (think about it! no overvoting problem!
Just Count the Votes!), multiple majorities would have required a
significant number of voters to vote for both Bush and Gore. How
likely is that? No, we'd see Nader/Gore, or Bush/Buchanan or maybe
Bush/Libertarian, and some other combinations, much more commonly.
In any case, methods like this are a simple counterexample to the
nonsense Austen-Smith has written about. I haven't examined his math,
his results may be valid within the restricted field he sets, but the
serious problem with his paper and his affidavit is that he draws
unwarranted assumptions from Arrow's Theorem and from his own work.
His work is far from general, but rather was more appropriate when it
was written, a great deal of work has been done since then. It is no
longer reasonable for someone familiar with the current work to make
the claims he makes, and his testimony could be, I suspect, and
should be, I'd assert, impeached on that basis.
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