At 02:46 AM 7/29/2007, Juho wrote:
> > 49 A
> > 24 B
> > 27 C>B
>The numbers of this example are so unlikely to occur in real life
>that I modified the example a bit to get values that would be more
>probable. This was the first one that I found to be close enough to
>be realistic (maybe not yet fully realistic, maybe there are others
>that serve the strategic needs better).
It's a bit difficult to judge what is "realistic" without looking at
real election data, and we are short of real data even from polls,
since most polls are asking the question "Who's your favorite?"
I'm not familiar with what *is* known about real voting behavior,
beyond a few points. Real voters vote many different kinds of
ballots. In a large real election, there will be ballots that are
totally blank, and ballots with all choices filled in. Even if the
rules prohibit overvoting, there will be overvotes, and some of them
will be deliberate, either due to a misunderstanding of the rules or
a deliberate voiding of the vote. Faster than running back and
getting another ballot, and voters can be in a hurry to get back to
work or whatever. An absentee voter marks the ballot wrong and, oops!
Can't get another so easily....
Like many election examples, the imagined data has itself been
truncated. If we are showing actual vote counts, we are showing a
very small election, and small elections have different
characteristics than large ones. The possibility of ties or near-ties
is increased, for example, and this affects strategy. The voters and
candidates tend to know each other, and there is less polarization.
And if we are showing percentages in a large election, they'd better
not add up to 100% unless we are including all the reasonable cases
we would see. The first example is oversimplified, for sure. Let's
look at how Juho has extended it.
I'm going to take Juho's example and edit it to add the complete
preferences, he omitted the equalities and I like to be explicit.
Truncating is the same as rating all the other candidates equal last.
I'm also spreading out the fields and putting them in columns so that
rank is clearly indicated
>30 A > B=C
>9 A > B > C
>6 A > C > B
>14 B > A=C
>8 B > C > A
>2 B > A > C
>25 C > B > A
>5 C > A=B
>1 C > A > B
I'm now quoting Juho out of sequence.
>I tried to keep the original number of first place supporters of each
>candidate. => 49/24/27. But I had to assume that some C supporters
>will truncate (since some B voters did so too) and as a result the
>number of A supporters had to be dropped to 43. In order to make C
>win B I donated these votes to C. => 45/24/31.
What is truly odd about this is the high number of truncations from B
supporters. It's the third most common vote.
Let's assume that the candidates are on some single axis. In major
elections, this is likely to be true, it is a simplifying first
assumption. In reality, there is more than one axis, and so
candidates who are, for an individual voter, close on one axis may be
far on another, and how the voter votes may thus seem inconsistent. A
otherwise-liberal who is morally opposed to abortion, for example,
may neglect the abortion axis except within pairs where the
candidates have the same position, in which case the
liberal-conservative axis comes into play.
Nevertheless, barging ahead with a single-axis assumption, who is the centrist?
Aside from sheer laziness -- and we've already selected out much of
that since truly lazy voters don't vote except where it is illegal to
not vote (a concept I detest, since not voting can be presumed to be
a vote equating all candidates, and there are non-coercive methods of
making sure that this is truly the case) -- truncation indicates a
strong preference between the marked candidate and the other two,
with a weak preference between them.
I've been contending for some time that in order to understand
election methods, even if they do not collect preference strength
information, we should posit it. Otherwise vote patterns are rather
arbitrary. We see, in places, comparisons of election methods that
are utterly concerned about what might be called the Satisfaction Sum
criterion (the method chooses the candidate who maximizes overall
satisfaction with the result) or the Satisfaction Count criterion
(the method chooses the candidate who maximizes the number of voters
who are at a chosen level of satisfaction or higher, also called
Approval). For brevity, we could call these the Range Criterion and
the Approval Criterion, but they should not be confused with the methods.
The reason why these criteria aren't mentioned and considered in
evaluating election methods is that we are accustomed to studying
methods by positing votes. And so we don't have any information about
these criteria. Except that, for example, with the Majority
Criterion, most writers *do* assume some kind of invisible
preference. But what is lacking is the far more informative
assumption of preference *and* preference strength. Otherwise,
without preference strength information, the analyst is equating a
strong, maximal preference, unshakeable, with an extremely weak
preference, so weak that the voters' vote is really a random choice
made at the time of voting. There is actually no preference at all.
There are those who claim that Range Voting is problematic because
there is no way of comparing the "utilities" expressed by the voter,
between voters. However, we can posit utilities just as easily as we
can posit votes, and we can posit them on an absolute scale that *is*
commensurable. Yes there is an assumption underneath that which may
not be true, but it is an assumption that democracy depends on. It is
the assumption that the opinion of every voter is equally valuable;
underneath this must be an assumption that the *range of welfare
possibilities* for every voter is equal.
In my writing on this, I call it the "first normalization." When we
select the utilities for candidates in preparing a study, we would
place these utilities on a scale where one end is "the worst possible
thing that could ever happen," and the other end is like that, only
the best." In real elections, generally, the absolute utilities will
be clustered in the middle somewhere, usually. And then there will
be, in the votes cast, some kind of normalization, which may or may
not be full.
We will see Range ballots where the voter votes low scores, for
example, for all candidates. Ballots like these will produce
different results with the Range Criterion and Approval Criterion, if
the approval cutoff is set at the mean rating for all candidates. So
a vote of Bad will be considered "Approval," by this criterion. There
are arguments that this is, indeed, what we should do.
When we are studying election methods, we are usually judging them by
some standard we presume best, such as maximizing the number of
people who prefer the candidate. Certainly we should include the
Range Criterion and Approval Criterion in our consideration.
Ranked methods without preference strength information inherently
will fail Participation, because if the voter expresses a preference
that is actually weak, it is treated as strong, or as being of middle
strength, and thus can warp the outcome such that it worsens for the
voter by voting. If I've got this right, the problem of Participation
is inherent with ranked methods for the reason described.
With the truncated votes here, the expressed vote is then treated as
having maximal strength. This is almost certainly overstated, yet the
ranked method leaves the voter with no alternative. If the voter's
normalized utilities for ABC are 910 in Range 9, the truncation is a
very reasonable vote, but if the voter does not truncate and votes
A>B>C, the voter is effectively voting as if the rating for B were 5.
That's a large distortion. And ranked methods do encourage this
distortion. The voter *does* prefer B to C.
Whether or not to use Range methods in public elections is a complex
question, particularly because of the possible problem of strategic
voting (though that appears overstated) and of normalization as well
(the alleged incommensurability of the utilities), but this is quite
different from avoiding its use in comparing election methods.
Whether in simulations or in exact studies, utilities must properly
underlie the value of election methods.
Back to the question of "Who is the centrist?"
We have here a disagreement by the electorate as to who is in the
middle. This is completely normal, because supporters of the middle
candidate will not agree on who is in the middle (in their own rankings).
If the election were choosing the "middle" candidate, who would it
pick? Consider it an approval election, with = votes being votes for
both candidates as in the middle.
A B C
A: 39 6
B: 16 22
C: 1 30
tot: 17 69 28
If we use the standard that equalities are not votes for middle, then we get
A B C
A: 9 6
B: 2 8
C: 1 25
tot: 3 34 14
Now, supporters of the middle candidate will disagree on who is in
the middle, because their judgement, inherently, will be individual.
If we assume an exact centrist candidate, half the voters will
consider the left to be the middle candidate, and half will consider
the right to be the middle.
The single vote from a C supporter that B is in the middle is
anomalous and relatively unrealistic, and this shows, actually, how
the original rankings were even more unrealistic. While real
elections will have anomalous votes, its introduction here, to assume
that a C voter will truncate because some B voters did, ignores the
fact that supporters of a centrist candidate can still have a large
distance from one side, if that candidate is closer to the other
side. The B truncations are realistic, the C not.
Clearly B is the middle candidate, overall, it's not even close, and
we can infer, further, from the B votes, that B is closer to C than to A.
>Vulnerability to the margins strategy was kept => similar cycle with
>appropriate differing strengths with margins and with winning votes.
>One C>B voter can change the result by voting B>C.
Thus reversing preference, considered undesirable. However, ranked
methods provide only one way to raise a candidate up in the vote, and
that is to reverse preference. In Range, as an example, a rating for
a candidate can be raised up to the level of another candidate,
without reversing preference. While this is not considered "sincere,"
neither is it "insincere," in that it is only asserting a smaller
preference, something that ranked methods don't even allow. Rating
B=C means that "Compared to my preference for both A and B, my
preference for B>C is negligible. If I think the real pairwise
election is between A and B, then my vote for C is really moot,
unless it harms B. Range methods would allow the voter to vote for C
without harming B. Ranked methods typically don't allow that.
To understand voter strategy and election methods, we must understand
how underlying satisfaction expectations relate to votes, and we must
also integrate how election probabilities relate to votes. Using the
Range or Approval Criteria allow these things to be quantified, and
without quantification, deciding what is "better" boils down to
trying to satisfy a list of criteria, known to be incompatible with
each other (and they are, if we restrict ourselves to ranked methods
and single ballot elections), without any objective standard for
rating the criteria themselves.
It's a formula for endless argument.
>It looks to me that B must be more centric than C.
Well, from the votes, it is totally obvious and clear. The division
of the A voters on this question is a bit puzzling, but it is
explained by the introduction of another axis of comparison that is
driving it. This axis does not affect the C voters, because they
align with B, relatively, over it.
I think looking at three-candidate elections as containing votes for
who is in the middle is interesting.
> I expect A voters
>to truncate since they are not interested in the right wing internal
This was the comment that first motivated me to respond here. At
first I thought it unreasonable, but, in fact, it is reasonable. B is
some distance to the right of center, so Juho's description is
accurate. For many A voters, B and C are both far to the other side.
In a method which allows the expression of preference strength, I
think we would see this clearly, if voters didn't exaggerate.
> B voters truncate since many of them are so close to the left
>wing that A and C are about equal in preference to them. C voters do
>not truncate much since for them the other right wing candidate B is
>clearly better than A.
>The most unrealistic point in this (one step more realistic) scenario
>is maybe the fact that so few A supporters find B better than C
>(although as I said, B appears to be closer to the centre than C).
>But let's go forward.
Yes. However, the introduction of another axis explains that. There
is some other issue on which B and C disagree that is of importance
to a subset of the A voters. And the A voters disagree among
themselves on this issue.
I gave an example above, abortion. Perhaps B is libertarian, really,
and opposes coercion, whereas C is more traditionally "conservative,"
which can be just as coercive as the supposedly high-tax
big-government position of the liberals.
And then we have the left divided into those who dislike coercion and
those who are quite willing to impose it for the public betterment.
(In reality, this is usually an argument over what coercion is
*necessary,* the libertarian position tending toward a stricter
definition of necessity, the authoritarian one toward an easier
assumption of necessity.)
So it's not only realistic that factions truncate, thus equating two
candidates to bottom place, but that they also disagree as to who is
in the middle. A two-party system makes this more rare, because the
big parties have amalgamated positions and thus define a major axis:
which party do you support, with lots of consequences for the answer,
because of how power is exercised.
When we get multiparty systems, it gets hopelessly complicated. Some
think that an argument against multiparty systems, but it isn't.
Reducing the complex choices of modern life to Party A or Party B
creates chaos on another level, the chaos of major effects from minor
causes. It's inherently unstable, though it can appear otherwise. If
the parties are really quite close to each other, if they are really,
in the universe of parties, quite centrist, then a flip from one
party to another has less effect, making the system more stable, but
also making the parties into Tweedledum and Tweedledee for a
significant number of voters, who then express their utilities by not
voting, it isn't worth it. Of if they vote for other reasons, such as
local elections that they care about, then their vote in the election
of concern is useless, chaotic, or can harm the outcome, if they
cannot express real preference strengths or participate in a way that
makes their vote count.
And a strong two-party system avoids the real question by deferring
it. How does society make decisions about how to coordinate and
cooperate for the common welfare? Putting the decisions into the
hands of two parties defers the question and makes it into "How does
the majority party make decisions about...." and "How do the two
major parties come to agreement to truly maximize common welfare?"
So, then, if we consider each party, how does *it* make decisions?
Does it do so democratically? What methods does it use?
Very few methods, I'd say. Primary elections have become common; it
is not clear to me that this is any better than the old smoke-filled
rooms, except for health reasons. Primary elections, indeed, would
tend toward radicalizing the parties, making them no longer centrist,
increasing the differences between them, bringing each party into the
center *of its wing* or even toward the more radical side of the
wing, because that side tends to be more motivated.
It's a mess, and we often think of, as solutions, proposals that
actually make things worse, because we don't understand how to
evaluate elections. We think that primaries are "more democratic,"
yet the result can be seriously harmful effects on the overall
satisfaction of the public. If we use the Approval criterion, this is
obvious. It we have two large parties roughly at parity, if the
rightist party nominates a candidate who is "centrist" on the right,
this candidate is at 25% on a scale, and this is quite "democratic."
And if the left party nominates a candidate centrist on the left,
this candidate is at 75% on that scale. (This is assuming equal
distribution. It isn't quite that bad, actually, because the
distribution will be, probably, a bell curve weighted toward the
overall center ... but the increased motivation to vote and campaign
from extremists can still push toward this position, effectively).
And then, no matter what candidate wins, 75% of the electorate
considers this candidate relatively undesirable, out of the universe
of possible candidates.
>This kind of observations apply to many strategic examples, not only
>this margins based strategy. The vulnerability of Condorcet methods
>to strategic voting is a fact but in most cases the vulnerabilities
>are quite marginal and seldom (or in some cases practically never)
>occur in real life.
That's not necessarily true. Truncation is a kind of strategic
voting, and it affects outcomes. Will voters reverse preference, however?
They do under plurality, and it is normal.
Consider this: if an election allows write-ins, voting the ranks in
the election is bottom-ranking every other possible candidate. There
are really, in public elections that allow write-ins, a very large
number of "candidates." Because of political realities, voters don't
write them in, they consider it a waste of time, and in a ranked
method, a wasted vote is possible. (In plurality, the waste is
guaranteed; allow overvoting, this changes.)
So almost every ballot, we can predict, incorporates preference reversal!
This could be changed! Suppose we have a Range election, and
write-ins are allowed, and so are runoffs under some circumstances.
There is a debate among Range advocates over how to treat specific
abstentions, that is, the voter votes, rating one or more candidates,
but does not rate all. Alignmnt with existing practice indicates that
you would min rate them. However, currently the default Range
proposal is a little more complicated than that. It is definitely
interesting to, at least for some purposes, exclude abstentions from
determining the average Range rating of a candidate. To allow this
candidate to therefore win has some obvious problems, starting with a
write-in candidate who gets 100%.
But what if we have a write-in candidate who gets 100%, and he is
written in by a very substantial chunk of the voters, say 25%. That
this candidate is not on the ballot, giving him a huge disadvantage,
he really should be there, but the process excluded him. Holding a
runoff between this candidate and the sum of votes Range winner would
(I'm not sure if this could be made compatible with my other
proposals to hold a runoff with a pairwise preference winner. True
democratic process does not limit the number of questions to be asked
the electorate, the electorate itself decides when it is ready to
make a final decision, and, unless there are special rules -- which
are generally compromises intended to speed up decision -- the final
decision is necessarily ratified by a majority. No matter what the
method used to get to that final nomination of a single candidate, it
is impossible not to get a majority winner, for the majority can
still reject the candidate if something went wrong with the process.)
(This inherent superiority of full democratic process over election
methods must be understood; election methods are compromises,
intended to make a decision out of a single snapshot of the
electorate, yet, in the real world, people make, when they have the
option, decisions over time as various options are weighed. People
who make major decisions in a snap without having reflected on the
options, which includes a kind of back-and-forth, are actually
disabled. But note that what can appear to be a snap decision can
reflect a long unconscious process, and it is only the final decision
point that is quick, where "intuition" leads the person to make a choice.)