[Election-Methods] Corrected "strategy in Condorcet" section

[Abd ul-Rahman Lomax]

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.

We have
         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
>battle.

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.

Yes.

>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 
make sense.

(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.)