[EM] Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 02:17 PM 11/8/2006, Chris Benham wrote:

>Abd ul-Rahman Lomax wrote:
>>
>>
>>As written, AV satisfies the MC, and the arguments I see
>>on this, so far, do not really address the issue.
>What issue? Since you don't support the "MC", why do you even care 
>if it does or not?

Because it is an argument frequently presented against Approval, and 
it is not correct. The MC has its legitimate application, so it is 
not exactly true that I don't support it. It can be applied outside 
that legitimate application.

But, in any case, the issue is *exactly* how the MC is applied to any 
voting method, and then how it is applied to Approval. As worded, in 
the only reasonable interpretation I can assign to the words, 
Approval satisfies the criterion.

It is enough at this point that it be established that the 
construction I put on the words is reasonable, not that it is the 
*only* reasonable interpretation. However, I don't think that the 
alternate interpretation being used by Chris is reasonable.

If a method allows voters to express a "strict preference," and 
Approval does, but it also allows voters to do something else, does 
this mean that voters who *have* expressed a strict preference, in 
the manner that the election method permits, are to be considered as 
not having expressed this preference merely because the method did 
not allow them to take the alternate path without expressing a strict 
preference?

Again, I don't think this is a complicated concept, and that it is 
receiving such entrenched opposition is simply a sign to me of 
reasoning from conclusions.

How can a voter express a "strict preference" in Approval.

Is there a means to do it?

That voters may do something else, which is express a "group 
preference" *is irrelevant*. Or is it relevant? How? What in the 
criterion covers this contingency?

If a majority of voters express a strict preference, can their choice 
fail to lose, in Approval? *Answer the question!*


>>To do so, you must define "strictly prefer."
>"Strictly prefer" means exclusively prefer.

Good. How does one express exclusive preference on an Approval 
ballot? Is it possible?

>Abd isn't the first sophist to try to argue that if a voter puts 
>more than one candidate in his/her
>preferred set, that must mean that he/she means to rank them all 
>equally in first place and so
>therefore if a majority don't put X alone in their preferred set X 
>can't be the majority favourite.

Calling an argument "sophist" neither increases nor decreases its cogency.

I'm not sure that Benham said exactly what he intended to say, but 
I'll take it as writ, just as we take ballots.

We assume that voters intend to do what they did. If they rank 
candidates equally, we must assume that this is what they intended to 
do. Approval only allows two rankings.

Benham switches the track in midsentence, I forget the linguistic 
term for this. I have never said that there can't actually be a 
"majority favorite" when a voter approves of more than one, indeed I 
would presume that the voter does usually prefer one to another. 
However, the method does allow the expression of exclusive, exact preference.

David Cary has raised or explained issues about what election 
criteria are and how they may be interpreted that do go to the point. 
He informs us that election criteria can be purely theoretical 
measures, and can assume, as a precondition, information which is not 
objectively determined in the real world, and that may *never* be 
obtainable. I.e., they may assume mental states on the part of the 
voter, and they may assume a model that translates mental states into action.

However, simplified explanations of the election criteria typically 
neglect these details. The full specification of the Majority 
Criterion, then, we have not seen here. And I don't really know where 
it might be.

Mr. Cary points out that, for example, IIA, can be interpreted in 
various ways, and then he gives names to the variations. So, too, is 
it possible that the MC can have various interpretations. Does any 
one of them have the right to be considered an objective evaluation 
of a method, with the others not being so?

No, this would be arguing over definitions. If we have an 
authoritative definition, we could refer to it. However, I don't 
think we have that.

What I've been saying is that, as the Majority Criterion is stated, 
it is quite reasonable to determine that Approval satisfies it. It 
depends on what "prefer" means. If it means to *express* a preference 
by an action that demonstrates it, then Approval satisfies the Criterion.

If it means to have some mental state such that, if asked "do you 
prefer A or B," the voter will indicate one of these, and what the 
voter actually votes on the ballot is irrelevant (i.e., the voter has 
a preference but does not express it because the voter wishes to do 
something else), then we could say that Approval does not satisfy the 
Criterion. But this has become a Criterion which is divorced from 
anything objectively verifiable. And this is not completely expressed 
in the statements of what the Criterion is, there are missing and 
necessary specifications. Indeed, to me, it seems that one would 
might to write the specifications with the method being tested in 
mind. So, essentially, the criterion would be designed with an end in mind....

I *know* Approval does not satisfy this criterion, so how can I state 
it so that this becomes clearly true?

>The criterion doesn't stipulate that the majority have to be willing 
>to pay a price or engage in
>some perhaps risky strategy to express their strict preference for X 
>above all others.

More spurious irrelevancy. If it is necessary for voters to brave 
gunfire to vote, this is also irrelevant to whether or not a method 
satisfies the criterion. If a tyrant is going to shoot them for 
"expressing their strict preference," this is irrelevant. The method 
permits it, it is the tyrant who does not.

Look, Benham, if you want to know how to argue cogently, or, perhaps 
more accurately, how to inform, read Cary's mail on the IIA thread.


>>Does Plurality allow the expression of preference? How?
>>
>The only "preference" the criterion is concerned with is the first 
>one, and that is the one that FPP
>allows voters to express.

Yes. And Approval likewise allows voters to express it, in exactly 
the same manner.

>   Making the comparison with Approval, if the voters are constrained to
>put a single candidate in their "preferred set", then of course that 
>candidate is their clearly voted
>strict favourite.

If they are not so constrained, but they do so anyway, they have 
freely indicated a strict preference, which is what the Criterion is 
concerned with. Again, constraints on the voter are irrelevant, 
unless they are built into the system. Plurality does not constrain 
the voter to express exclusive preference, voters can and do 
otherwise, in one or more ways. But they *can* certainly use the 
method to express exclusive preference, and that was the design 
purpose as well, though the design purpose is irrelevant.

And they can do the same with Approval.