[EM] Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 08:01 AM 11/2/2006, Michael Poole wrote:
>The Majority Criterion is an objective criterion.

It looks that way. When you look closer, there are some ragged edges. 
What does "prefer" mean? Is there a threshold in preference strength 
below which it is effectively the same "rating." I.e., the voter 
might make a choice, if forced to by the method, but really has no 
*significant* preference.

Further, it is alleged that Approval does not satisfy the Majority 
Criterion. It seems to me that this requires a few assumptions that 
have not been made explicit.

>   When you ask about
>preference strength, it becomes extremely subjective -- and attempts
>to normalize the subjective effects (for example, rescaling each
>voter's expressed preferences to a common minimum and maximum) obscure
>honestly expressed preferences.  While one can reasonably complain
>that objectively defined measures to not maximize subjective goals,
>the superiority of the subjective measure should be established[1]
>first.

Doublespeak, I'd say. It is quite clear that there is some basis for 
variation in preference strength. It's real. It is no more subjective 
than preference itself; simple preference has taken the complex space 
of voter expectation and has reduced it to a binary relation. A lot 
of data is lost.

Is that data of value? I've shown situations where it clearly is of 
value, where the Majority Criterion will clearly choose a winner who 
will be a disaster for the society. And historical examples can be shown.

>Ultimately, social utility is not a static function[2]; election
>results alter the function both directly and indirectly.

Yes, of course. But the very idea of elections is to derive some kind 
of conclusion from the state of the voters at the time of the 
election. This very idea is defective, that is, not optimal, but once 
we accept it, that further expectations will change after the 
election is irrelevant. The election is attempting to determine "the 
choice of the electorate." And we are attempting to define what that means.

Essentially, how is the choice made, and for what purposes and to 
what ends. If we don't consider the ends, but merely consider a very 
limited metric, on the argument that this metric is "objective," even 
though it is entirely based on subjective comparisons by all the 
voters, we end up with an artificially constrained result that will 
be distorted, under some conditions -- I would argue that it is 
commonly so -- away from optimum.

Of course "optimum" is a subjective judgement, unless there is a way 
to measure it. The only way that I have seen proposed is Social 
Utility. And Range is the method that attempts to predict this, using 
voter expectations and assuming that these expectations are, on 
average, related to the actual utility.

It's called democracy. It is an assumption that, more often than not, 
the people will be right. But, of course, this does partially depend 
on how we determine what the people want.

It is patently obvious that a very slight preference, the voter would 
be, really, equally happy with A or B, is quite different from a 
strong preference, where the voter will be devastated if A wins and 
happy with B.

You know, I've voted Democratic for a long time, but I was never 
truly *distressed* at a Presidential election result until 2000 and 
then 2004. I would not have rated the Dem as 99 and the Rep as 0. In 
2000, I was distressed, not because Bush was winning, but because the 
*process* was unjust, a result of a whole series of twists of 
Constitutional intent. Then, I hoped that Bush would be as he claimed 
to be, a "uniter not a divider." We have not had a President so 
divisive in my memory. What does this have to do with Range? By 2004, 
I *would* have been voting Range 99 or perhaps 98 for Kerry and 0 for Bush.

Yet my vote counts exactly the same as the vote of someone who has 
almost no preference, who is dithering up until election day as to 
whom to vote for.

Now, one may say, and it is said by Range opponents, why should my 
strong preference have any weight over the weak preference of another?

*Because strong preferences predict the relationship of the voter 
with the resulting government.* Ignoring strong preferences results 
in voter alienation. From it being "our" government, it becomes 
"their" government. And this is at the root of a great many social problems.

In no way should my strong preference outweigh the strong preference 
of another voter. And Range (and Approval) give all voters equality 
in strong preference. They can vote that way.

So if "prefer" in the definition of the Majority Criterion were 
worded "significantly prefer" -- so significant that it will clearly 
affect voting behavior -- Approval will satisfy the Majority 
Criterion. The only way that one gets Approval to fail the criterion 
is by assuming that there is a preference that is unexpressed. This 
is clear because it is claimed that Plurality satisfies the Majority 
Criterion. But if a majority of voters prefer C, but vote for A under 
Plurality because they don't realize that they are in the majority, 
and worry that B will win, we have a Plurality election which does 
not satisfy the Majority Criterion.

Essentially, Approval allows the expression of preference. Prefer A 
over B? Vote for A and not B. Same as Plurality. So Approval 
satisfies the Majority Criterion.

Range, however, does not, I think. But it does not because the 
Criterion itself totally neglects and ignores preference strength, 
whereas Range measures it.

>   Given the
>upset caused by the last two US elections, this feedback is perhaps a
>factor in your argument that an election should maximize social
>utility.

It's a general argument that does not depend on the last two elections.

>   However, I suspect negative feedback makes the system
>unstable by encouraging radicalization by opposing factions.  An
>unstable objective makes it more important to explain why that
>objective should be sought.

The present system is unstable, in my opinion. Range ought to be more 
stable, because it does not switch radically based on small 
perturbations. However, any single-winner method is vulnerable to 
instability. Parliamentary systems should be more stable, if elected 
by true PR. However, my own opinion is that instability is inherent 
when power and communciation systems are blended, because the 
blending causes amplification of majority opinion; there is feedback, 
and it is positive feedback. So small perturbations initially can 
radically swing the output.

Generally, negative feedback reduces instability....

>[1]- Any proposal to maximize social utility that is to be taken
>seriously in the US should avoid arguments that could be rephrased or
>paraphrased as seeking "the greatest good for the greatest number" --
>those are too easily comparable to communism, which had its own
>failures due to preference for subjective over objective measures.

Yes, that's true. However, the greatest good for the greatest number 
argument is an old one, and has been used by conservatives as well as 
others. The "rising tide lifts all boats" is a greatest good 
argument. It is arguing that what makes the rich richer also makes 
the poor richer. Maybe. Sometimes. Maybe sometimes it does the opposite....

>[2]- Suppose that 5% of the populace have no preference between two
>major candidates, 50% have a slight preference for one, 40% have a
>slight preference for the other, and 5% have an irrationally strong
>preference for the second.

"Irrationally strong" is the introduction of a judgement of 
preference. It is assuming that voters have a preference for the 
wrong reason. And then, of course, we should, it will be alleged, 
disregard that preference because it is irrationally strong.

But people with irrationally strong preferences have just as much 
right to have their preferences respected as anyone else. Indeed, I 
could argue that they should have more right than that of those with 
weak preferences.

I gave the pizza analogy. Suppose that the strong preference of the 
anti-pepperoni "voter" is "irrational." He fears that he will die if 
he eats pepperoni, and, since we are defining it as irrational, he 
will not die. Now, if 100% of the population will be reasonably 
satisfied with Mushroom pizza, should we choose Pepperoni merely 
because a majority -- perhaps a slight majority -- have a slight 
preference for it?

In the example given, if we do *not* disregard the strong preference 
of the "irrational" group, but if we have Range Voting, we end up 
with *100% of the electorate being satisfied by the election. This is 
how Range Voting is supposed to work. But it does not satisfy the 
Majority Criterion unless we follow the analogy with Approval Voting 
and claim that the meaning of "preference" in the Criterion is 
"strongly prefer." Strongly enough to rate the preferred candidate at 
maximum and all others at zero.

If a majority of voters have that strong a preference, their 
preferred candidate cannot lose. I claim that this satisfies the 
substance of the Majority Criterion. What is really true is that the 
Majority Criterion was not designed to deal with election methods 
where preference strength is considered.

It sounds good as long as we don't think about preference strength. 
Yes, it is just a Criterion, but it is intuitively obvious as a 
desirable criterion until we start thinking about preference strength.

I pointed out elsewhere how, sometimes, it is sound knowledge that 
leads to strong preferences. Voters, without knowledge, can be easily 
confused, all too often. Some of them have strong preferences based 
on other than knowledge, but this does not change the fact that 
people, for example, who personally know or who have other forms of 
sound knowledge about the candidates may have, as a result, strong preferences.

The only way that a majority can have a preference under Range and 
not have their preferred candidate win is if the preference is weak. 
And, by definition, then, they will not be seriously dissatisfied 
with the election outcome. They *must* have given a decent rating to 
the actual winner.

>   Include distasteful-to-somebody third
>parties as needed for rescaled ballots to reflect honest preferences.
>If the irrational strength of preference by 5% of people outweighs the
>slight opposite preference by 10% of the population, it seems more
>likely to push some of the 50% group to their own irrational extreme.

I don't find this cogent at all. At least I couldn't understand it. 
Could be my fault. Or it's late.