I find this fascinating.
At 12:45 AM 6/9/2005, James Green-Armytage wrote:
I was recently asked to clarify the statement on my web site that
approval voting fails independence of clones.
http://fc.antioch.edu/~james_green-armytage/vm/define.htm#clones
This was my reply. Debate is welcome...
It looks like Mr. Armytage is correct. Approval voting fails independence
of clones, as clones are defined. The problem is that the definition of
clones and the independence criterion, under that definition, *sound* like
reasonable criteria for a fair election, but they are not. As Mr. Armytage
notes, changing the definition of clone such that the two candidates in
question are truly as similar in electorate opinion as would be implied by
the term "clone," causes Approval to pass ICC.
First, I use a consistent means of adapting ranked ballot criteria to
non-ranked methods.
http://fc.antioch.edu/~james_green-armytage/vm/define.htm#nonrankedcrit
So, ICC definition is changed to this, for use in evaluating
non-ranked
methods:
1. Clones: A set of candidates such that for every candidate outside the
set, all voters either prefer the outside candidate to all inside
candidates, or prefer all inside candidates to the outside candidate.
It is this definition which is the problem. The most important problem with
it is the use of the word "clone." The definition does not adequately
specify the required similarity of voter preference that the word in
ordinary usage implies. Yet the failure of the definition is easily
overlooked, that is, it is easy to think that it is sensible to apply this
definition and the criterion to a fair election method and expect it to
pass. And if it fails to pass, there must be some defect in the method.
Logically, however, it is also possible that the defect is with the
definition and criterion.
2. Independence of clones: If a clone set has two or more members,
removing one of the clones should not have any bearing on whether the
winning candidate comes from the set. Likewise, adding a new clone to the
set should not have any bearing on whether the winning candidate comes
from the set.
When I read this, without looking at the example, and without much history
of examination of these methods in general, I thought, "Sounds good to me."
Failure example:
Preferences with approval cutoffs:
60: A>R>>S
40: R>S>>A
Right away, I thought: this is an examination of Approval using information
not expressed in the election. Yes, it still seems that the criterion ought
to apply, but no election method is going to, in all cases, produce a fair
result that can only be judged as fair based on unexpressed information.
Approval scores:
A: 60
R: 100
S: 40
R and S are clones. R is the initial winner. However, if you remove
candidate R, the winner is A.
Just for clarity, it may be useful to restate the chart without R, assuming
that voters would not therefore change their votes if presented with this
different ballot.
60: A>>S
40: S>>A
Because there are only two candidates, the election has reduced to standard
plurality. A is the plurality winner with either ballot set.
This situation boils down to noticing the fact that Approval can fail to
elect the plurality winner, instead electing a winner with wider approval,
which is what happens here with the addition of the compromise candidate R.
In this election, A is a highly polarizing candidate. It is this fact which
allows the "failure" to occur.
I have proposed a modified version of ICC such that candidates
must be
given identical cardinal/approval scores by all voters to qualify as
clones, in addition to the standard qualification rule. I believe that
approval and cardinal pairwise both pass this modified version of ICC, but
not the standard ranked ballot version.
It should be remembered that the results of these analyses will be read by
people without sophisticated knowledge of the exact terminology used, and
in this particular case, two words stand out as misleading. The first is
"clones" as defined. It implies total similarity, yet a crucial
dissimilarity has been allowed to remain, that the "clones" can be created
from sets of oppositely-preferred candidates. The proper usage of "clone"
would be as modified in Mr. Armytage's proposal.
The other term is "failure." To fail to satisfy a criterion implies a
defect in a method. In this case, the "failure" to satisfy the criterion,
if it is to be considered as a defect, might be the defect in the
criterion, which incorporates the hidden defect in the definition of clone,
not a defect in the method. Instead, it is merely a corollary of a known
*characteristic* of the method, which is that it can choose a compromise
candidate over a majority favorite. It would be simpler to state that
Approval "fails" to elect the majority favorite, i.e., in the complete
election as described, where R is obviously a unifying candidate enjoying
universal approval, A is a candidate who is favored by a majority but
disapproved by a minority, and S is the polarized candidate of the same
minority. Everyone will agree that S should lose.
The matter becomes clearer in some ways if the election is closer. If the
electorate is just about evenly divided between two candidates, and it is
highly polarized rather than being merely a small preference difference,
electing either candidate could be quite harmful. It may be desirable under
such a situation to elect a compromise candidate, someone more widely
trusted. But in a polarized electorate with plurality voting, overvotes
discarded, such a candidate will lose -- unless people vote insincerely --
and may not even bother to run.
Approval voting is promoted to solve exactly this problem, so it is hardly
surprising that it works as intended!
Some of the discussion of election methods on this list and elsewhere is
rather divorced from practical considerations and consequences. This is
appropriate to a degree, but I've mentioned before that, pedagogically, it
leaves a great deal to be desired. It is difficult to learn arbitrary
information. If Election Methods experts would hope to become a priesthood
with esoteric knowledge not available to the common person, hoping somehow
that the ignorant public would then consult them, proceeding in this way
will help the cause.
I've been filling out tax forms recently, and it seems they become more
complicated year-by-year. I just filled out the 2002 Child Tax Credit
Worksheet, which is a mass of seemingly arbitrary calculations. There it
is, in front of me, with each line spelling out exactly what is to be
entered into it, followed by a series of instructions like "If the answer
is Yes, then enter 0 on line 12, skip lines 13 through 14 and go to line
15, otherwise, add the number on line 3 on page 4 to the number on line 11
and enter it on line 13 and then proceed to line 14." After 14 pages of
this, one comes up with a number to enter on Form 1040.
Let's say that I have about 10% confidence that I did it correctly. In
order to get to that confidence level, I had to go over the form and fill
it out three times. I'd say that there is just about no way that an
ordinary reader is going to make any *sense* out of the form. I'm sure
there is a good reason for each of the entries and procedures. But the
presentation is so complex as to make it impossible to understand the
result, to know if it is reasonable. And, as is typical, there is no
overall explanation of *why* the form is going through its quite complex
processes. Without that, I do not have the additional information necessary
to make the validation judgement that it has been done correctly. Applying
this to the present situation, if the language is confusing, no matter how
accurate it may be to a specialist, it makes it much more difficult to get
that elusive "sense of rightness" that typically accompanies a correct
understanding, leaving the reader with a sense of confusion *even if the
text has actually been understood correctly.*
Among specialists, language can be arbitrary and words can be, indeed often
must be, defined differently than in common usage. However, if there is any
hope to use the outcome of the specialist deliberations in modifying
real-world practices in a democracy, it would be more appropriate to use
language that does not *contradict* ordinary understandings of words. It is
often necessary to add precision to words in specialist usage. However, the
usage of "clone" here (in the original definition) does the opposite, it
includes something which would be excluded in common speech. That is
probably why some people had a difficulty with the statement that "Approval
fails ICC." As defined, it does indeed fail, but, again, this is not a
"failure" in the ordinary sense. It would be more neutral to say something
like "Approval disregards the ICC criterion, which was designed for ranked
ballots, but satisfies a more specific criterion using definitions arguably
more appropriate to approval ballots."
Yes, more words. But sometimes if one is going to communicate clearly, and
especially precisely, it can take more words. Of course, a good writer
could probably say what I said in many fewer words. I wish I was a better
writer; as it is I find that the only way I can write cogently *and*
briefly is to spend much more time with it and I already spend too much....
Which is why I've been filling out 2002 tax forms in 2005....
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