[Election-Methods] Dopp: 15. “Violates some election fairness principles ."

[Abd ul-Rahman Lomax]

>15. Dopp: “Violates some election fairness principles
."
>
>This charge reveals either a general lack of 
>understanding, or intentional 
>miss-representation. Every single voting method 
>ever devised must violate some "fairness 
>principles" as some of these criteria are 
>mutually exclusive. Dopp's example in appendix B 
>of "Arrow's fairness condition" (the Pareto 
>Improvement Criterion) completely misunderstands 
>the criterion, and gives an example that has no 
>relevance to it (and contrary to her 
>implication, IRV complies with this criterion). 
>IRV works essentially the same as a traditional 
>runoff election to find a majority winner. When 
>the field narrows to the two finalists in the 
>final instant runoff count, the candidate with 
>more support (ranked more favorably on more 
>ballots) will always win. Some theoretical 
>voting methods may satisfy some "fairness' 
>criteria, such as monotonicity, but then violate 
>other more important criteria such as the 
>majority criterion, or the later-no-harm criterion.

This is typical argument from FairVote. Read it 
carefully. Without going into the truth of the 
remainder of the paragraph, the remainder of the 
paragraph confirms what Ms. Dopp wrote. Sure, 
it's a possible argument that "all voting methods 
violate some election fairness principles," but 
... Ms. Dopps statement still stands. There are a 
number of issues here, and it's something that 
has fooled even experts, so please bear with me.

Arrow's theorem has been widely interpreted as 
"no election method is perfect," or "all election 
methods must violate at least one of a list of intuitively fair principles."

However, Arrow's theorem was actually very 
limited, and Arrow made the decsion not to 
consider as "voting methods" such basic methods 
as Approval Voting and Range Voting. Arrow 
recently actually repeated this, that he does not 
consider Range a "voting method." This is because 
it expresses preference strength information, and 
Arrow concluded that there was no substance to 
this. It's a very complicated debate, in fact. To 
Arrow, all that matters is whether you prefer one 
candidate to another, and how strongly you prefer 
is irrelevant. Yet in ordinary human 
decision-making, if we lived by the black and 
white rules of pure preference, we'd be making 
some pretty bad decisions! There is more recent 
work on this that has not yet been widely 
accepted, in particular a paper by Dhillon and 
Mertensm, published in Econometria, Vol. 67, No. 
3 (May, 1999), pp 471-498, purports to prove that 
what they call Relative Utilitarianism, but which 
is identical to the Range Voting proposed by 
Warren Smith in his later work, is the unique 
solution satisfying redefined Arrovian criteria 
that allow for equal ranking and preference 
strength information to be expressed.

Range Voting and Approval Voting both satisfy, in 
fact, reasonable interpretations of all of 
Arrow's fairness criteria; however, Arrow doesn't 
consider either of them "voting systems," and 
they do not meet the definition of voting system 
used in his proof. (Actually, the proof doesn't 
describe voting systems, as such, but merely the 
conversion of a set of individual preferences 
into an overall social ordering of options. 
"preferences" means a strict ordering of all the 
options. No equal preferences allowed, and no 
consideration of preference strength.

This matter of preference strength is crucial. 
For example, several possible voting methods, 
excellent in many respects, fail the Majority 
Criterion. Sometimes FairVote tries to equate 
this with failing "Majority Rule," but, in fact, the two are quite different.

There are some differences of opinion as to how 
to interpret the Majority Criterion. When Woodall 
did his work on it, he was considering only 
preferential voting systems, with no equal 
preference allowed. And the input to the voting 
systems he was describing was a strict preference order.

The Majority Criterion can be stated as: if a 
majority of voters place a candidate at the top 
of their preference listings, that candidate must 
win. This is an example of a criterion that 
seems, at first glance, to most, to be 
intuitively fair and proper and, even, necessary, 
and it sounds like majority rule, and, indeed, there is a connection.

This is the connection. If a majority of voters 
express a vote to prefer A over all other 
candidates, A must win. This is a variation on 
majority rule. The essence of majority rule is 
that no decision is made except by the explicit 
consent of a majority of those voting. If a 
voting system can choose a winner without the 
consent of a majority of those voting, it 
violates what I call the Majority Rule Criterion.

Does IRV satisfy the Majority Criterion? Sure. If 
a majority of voters vote for a candidate in 
first preference, that candidate immediately wins 
the first round. And only one vote is allowed in 
the first round, the election rules always 
prohibit approval-style voting, so MC compliance is assured.

But does IRV satisfy the Majority Rule Criterion? 
No. In fact, there is only one election method in 
common use for public elections that does satisfy 
it: top two runoff. (It *fully* satisfies it if 
the rules allow write-in votes, if "vote" is 
interpreted as in Robert's Rules of Order, and if 
it is possible for the runoff to also fail if no 
candidate gains a majority in the runoff. In most 
runoffs this is possible, if extraordinarily 
rare, but I don't know about the actual rules if 
there is majority failure in the runoff. Robert's 
Rules would say keep at it. Repeat the balloting 
until you have a majority winner.)

Top-two runoff is *also* not a voting method by 
Arrow's definition, because it isn't 
deterministic from a single static set of 
preference profiles. Voters can actually change 
their votes! Robert's Rules, in fact, points out 
that preferential voting "deprives" voters of the 
ability to base later votes on the results of 
earlier results. IRV is, in fact, a plurality 
method, *unless you continue to require a true 
majority." In Australia, in most Preferential 
Voting elections, they do require an absolute 
majority. They manage this by requiring *full* 
ranking of all candidates, or the whole vote is 
considered spoiled and not part of basis for 
majority. Imagine that in District 9 in San 
Francisco, with 22 candidates! This, however, 
represents coerced votes, it is difficult to call 
those lowest preference votes "consent."

Later-No-Harm is FairVote's favorite election 
criterion. That's because the peculiar design of 
sequential elimination guarantees -- if a 
majority is not required -- that a lower 
preference cannot harm a higher preference, 
because the lower preferences are only considered 
if a higher one is eliminated. But later-no-harm 
is a quite controversial criterion, many think it positively undesirable.

Woodall, who named Later-no-harm, wrote: "... 
Under STV the later preferences on a ballot are 
not even considered until the fates of all 
candidates of earlier preference have been 
decided. Thus a voter can be certain that adding 
extra preferences to his or her preference 
listing can neither help nor harm any candidate 
already listed. Supporters of STV usually regard 
this as a very important property, although it 
has to be said that not everyone agrees; the 
property has been described (by Michael Dummett, 
in a letter to Robert Newland) as "quite 
unreasonable", and (by an anonymous referee) as "unpalatable".

Indeed. Later-no-harm interferes with the process 
of equitable compromise that is essential to the 
social cooperation that voting is supposed to 
facilitate. If I am negotiating with my neighbor, 
and his preferred option differs from mine, if I 
reveal that some compromise option is acceptable 
to me, before I'm certain that my favorite won't 
be chosen, it is utterly ruled out, then I may 
"harm" the chance of my favorite being chosen. If 
the method my neighbor and I used to help us make 
the decision *requires* later-no-harm, it will 
interfere with the negotiation process, make it 
more difficult to find mutually acceptable solutions.

Later-no-harm is actually one of the few common 
criteria that IRV satisfies, along with the Majority Criterion.

So what about that Majority Criterion? Is it 
desirable? Well, any method which considers 
preference strength will fail the Majority 
Criterion, it must. Suppose that 51% of the 
voters have a trivial preference for A over B, 
they really don't care, but if you ask them, they 
would say they prefer A. The other 49% strongly 
prefer B. Maybe this is a choice of foods, and 
they are allergic to B. What's fair? Majority 
Criterion, or maximized overall satisfaction with 
the result. As this example was stated, the 
choice of B has no significant harmful effect on 
the majority and, in any healthy society, if they 
are informed, say by a Range poll, of that strong 
preference of the minority, and especially if it 
is explained to them, they will quite cheerfully 
vote, if directly asked, "Shall we choose B?", yes. Quite probably unanimously.

Majority Rule, strictly, involves asking a single 
question that can be answered yes or no. However, 
for efficiency, we do allow multiple questions; 
but then the question arises, what if multple 
conflicting choices both receive a Yes vote? 
There is a standard legal answer for this: the 
one that has the most Yes votes will prevail. 
Approval Voting. But, technically, it fails the Majority Criterion.

*When* does it fail the MC? Only if there is more 
than one option approved by a majority. In that 
case, it is possible that the majority actually 
preferred the option that received less Yes votes 
than the other, because whenever a person votes 
for more than one option, the preference between 
those options is concealed (in Approval voting, 
or those multiple conflicting Ballot Questions). 
FairVote will be very quick to tell us that 
Approval fails the Majority Criterion, but this is what that actually means:

In Florida 2000, suppose that voters could have 
voted for more than one. Voters who preferred 
Nader might also have added a vote for Gore. This 
is really an alternative vote, because it is 
never operative as more than one vote in any 
pairwise election. Naturally, this violates 
Later-no-harm, because, in theory, the extra vote 
for Gore could cause Gore to beat Nader. I'm sure 
that the Nader voters would have been very 
worried about that, don't you think? But what 
about the Majority Criterion? Well, the only 
reasonable possibility at all would be that many 
voters approved both Gore and Bush. More than 
didn't approve either Gore or Bush. We can be 
sure that there would be a lot of the latter, who 
aren't going to vote for a major party candidate 
come hell or high water. But the reverse, voters 
who vote for both frontrunners in a partisan 
election? Let;s say this would be rare and leave 
it at that. And not only rare, but harmless.

Approval Voting, as I mentioned, isn't a voting 
system by the definitions of Arrow's theorem, but 
if the definitions are generalized in a 
reasonable way, Approval does meet all the 
conditions of Arrow's theorem. It should, it's a 
Range method, the very simplest, and Range methods meet those conditions.

IRV can drastically fail to elect a candidate 
preferred to the eventual IRV winner by a large 
majority. It meets the Majority Criterion, yes, 
but if fails Majority Rule, and badly, and, in 
this case, not only Majority Rule, but the very 
basic rule, the king of preferential voting 
rules, the Condorcet Criterion. If there is a 
candidate who is preferred to all other 
candidates by a plurality of voters, considering 
each pair of candidate separately, this candidate 
must win. Approval fails the Condorcet Criterion 
for the same reason it fails the Majority 
Criterion. Essentially, it fails it for a good 
reason, it does something better.

What does "better" mean? It's only fairly 
recently that seriosu work started to become 
widely known on this question. There is a method 
of estimating the overall satisfaction of an 
electorate with an election, and, in fact, it 
shows Range Voting to be optimal precisely 
because Range Voting, if we could somehow insure 
totally accurate sincere votes, *is* the method 
of measuring satisfaction. There is some very 
serious math behind this, and a lot of work, 
mostly by mathematicians and economists. The 
political scientists mostly got stuck with 
preference, but economists worked with game 
theory and how to make optimal choices.

What is the point of all this? If we are going to 
reform elections, there are much better methods 
to choose than instant runoff voting, and, it 
turns out, they are simpler and cheaper to 
implement. Approval costs practically nothing: 
just count all the votes. Bucklin voting deserves 
another look: it was Widely used in the U.S., and 
it was popular, and real voters, apparently, 
don't pay much attention to the Later-No-Harm 
criterion. The "harm" in Bucklin only occurs if 
your favorite doesn't win by a majority in the 
first round. The only difference, really, is that 
Bucklin doesn't eliminate any candidates. It just 
counts all the votes. It's quite like Approval, 
but ranked. "Instant runoff approval." It is more 
efficient at finding majorities than IRV, because 
IRV does *not* count all the votes. (When an 
election reaches the last round without having 
found a majority of all the votes cast, there are 
the lower preferences of the remaining two 
candidates that have not been uncovered yet. 
These votes are never counted. -- but the San 
Francisco reports do show them, so it is possible 
to do Bucklin analysis on those San Francisco IRV elections.)

Contrary to the attack on her integrity from 
FairVote, Kathy Dopp does explore these issues in 
her report. The one point, though, that is often 
overlooked, is that IRV is being used to replace 
top-two runoff, a far superior method from the 
point of view of democratic process, and one that 
can easily, with little or no expense, be made 
even better, i.e., more efficient at finding 
majorities without requiring a runoff, as well as 
more likely to choose the best candidates if 
there must be a runoff. Hybrid methods are quite 
possible that would perform essentially ideally, 
satisfying the requirements of democratic process 
-- which Plurality and its sister IRV don't -- 
and all that it takes is the political will to 
start examining the alternatives with clear eyes 
and open minds. We can start by looking at how 
existing methods are performing. Not much study 
has been done on top-two runoff. And not much 
study has been done of how IRV is actually 
performing. That needs to be remedied. I can 
guarantee our readers this: FairVote is not 
interested in objective analysis of how IRV is 
performing, it's on a mission, and it does not want to be distracted by facts.