[EM] New MN court affidavits by those defending non-Monotonic voting methods & IRV/STV

[Abd ul-Rahman Lomax]

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.