[EM] RE : Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 11:06 AM 11/2/2006, Kevin Venzke wrote:
>--- Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > I've been realizing just how defective the Majority Criterion is.
> > People tend to assume that the Majority Criterion is an important
> > characteristic of any proper democratic election system.
>
>I suspect that many people would insist on a majority favorite being
>elected at least if the method collects enough information to
>determine who this candidate is.

Most methods do collect that information. But if 
a Majority preferred candidate fails to win under 
Range, it is necessarily that they, on average, 
also rated the Range winner quite high.

Sure, people will insist on this. Because they 
have confused the Majority Criterion with 
Majority Rule. But elections are defective when 
they attempt to choose between more than two choices.

Consider this: an election is held in two phases. 
The first phase is Range. The second phase, to 
take it to the extreme, is a ratification phase, 
in which the question is presented, "Shall the 
Range winner be elected to the office?"

Would this election satisfy Majority rule? Yes, necessarily it would.

Let me tell you, I've seen voting in actual 
situations where there was a status quo A. And 
objections to A were raised. And people, 
long-time members of the organization, and A had 
been the status quote for perhaps fifty years, 
literally said, "Over my dead body." After 
discussion, a poll was taken that was essentially 
an Approval polls. A variety of proposed 
alternatives to A, plus A itself, were presented 
and the members were asked to vote as to which of 
these were acceptable to them. I think it was 
perhaps 80% for A. But there was another option, 
B, where the vote was, in think unanimous 
approval, or maybe unanimous minus one. Then the 
question was asked, "shall we change to B?" The 
vote for this motion was unanimous in favor.

You cannot predict what people will actually 
prefer until they have good information about 
what everyone else prefers. In the organization 
in question, unity was valued. They did not want 
to needlessly neglect the strong preferences of a 
minority. And they have been a strong 
organization for many years largely because of this.

> > Yet the
> > Criterion itself suffers from a number of serious problems.
> >
> > (1) It is clear that any method which satisfies the Majority
> > Criterion cannot maximize the expected value of the election. Range
> > is the method which directly does the latter, and this is directly
> > connected with its non-satisfaction of the Majority Criterion.
>
>However, it is possible that there is no real method that can "maximize
>the expected value of the election," unless you just mean to maximize
>the value among all possible methods.

No, Range does this. If we assume that voters 
express their expected value for the various 
candidates, the expected value for the voters, 
collectively, is the sum of the individual expectations.

Objections to Range are often based on the 
assumption that voters will distort their 
expression for strategic purpose. However, I've 
shown, I believe, that this is an oxymoron. The 
alleged distortion is an alleged strategic rating 
of a serious competitor to the favorite at zero, 
even though, in the scenarios proposed, they 
actually only mildly prefer their favorite to the competitor.

Yet, the scenario assumes, they are willing to 
lie about their preferences in order to gain the 
election of their favorite. I claim that this 
would be evidence that they are either mentally 
ill or they actually strongly prefer the 
favorite. It might be because their favorite is 
from their party, rather than because of the 
individual characteristics of the candidate. But 
preference strength and Range ratings include 
such considerations as party affiliation, at least for some....

>I don't think it is fair to say that Range "directly" "maximizes the
>expected value of the elections." I would grant that Range is equipped
>to do this better than other methods due to the ballot format, though.

Range is designed to do exactly this.

Note that a Range ballot can be analyzed and used 
for other methods. It collects the most 
information of any ballots I've seen proposed.

>[...]
> > Looks to me like Approval *does* satisfy the Majority Criterion.
>
>I can see nothing at all wrong with that interpretation, but personally
>I don't like to imagine that the Approval voter is only submitting
>first preferences.

Neither do I. But the point is that if they have 
a preference, they are able to express it. They 
can also do something else, which is to prefer a 
block of candidates rather than just one. This is 
an additional freedom. In standard Approval, they 
cannot both prefer a block and express a 
preference within a block, but, of course, they 
can't do this with Plurality either. And, as I've 
noted, it is commonly stated that Plurality satisfies the criterion.

We can say that Plurality satisfies the criterion 
if we assume that the voters have expressed their 
preference, without any strategic considerations 
at all. I.e., they vote for their favorite, and 
not for their favorite among the top-two. Which, 
of course, is seriously harmful behavior, in at least some ways.


> > This is important because many writers assume that the Majority
> > Criterion is some kind of gold standard for elections, and when it is
> > asserted that Approval fails to satisfy it, this can be and is
> > considered a fatal argument, or at least a serious defect of Approval.
>
>I don't feel that Majority needs to be satisfied under Approval, in
>order to be publicly acceptable.

My argument for Approval is simple: tossing 
overvotes is unjust, it has historically done a 
great deal of harm in suppressing actual voter 
intentions. Sure, some overvotes, maybe even 
most, are errors, and we can't tell which of the 
two candidates, if it is two, were intended. But 
we can be pretty sure that it was one of them!

By tossing the vote, the method has made the 
voter abstain from all pairwise elections. By 
using it, the only pairwise election from which 
the voter abstains is the one between the two 
votes. Much less harm is done by not discarding the vote.

It has also been argued that prohibiting 
overvoting helps prevent election fraud. All I 
can say is that it seems to me that it opens the 
door to election fraud more than it closes it....

The argument for prohibiting it seems to be that 
voters should make a clear choice. The reasoning 
behind this escapes me. Once again, it gives 
value to a slight preference, equating it with a clear one.

Implementing Approval is trivial, just strike out 
the few lines in the election code that prohibit 
overvoting. Everything else stays the same. 
Approval is already standard in some states where 
there are two conflicting initiatives on the 
ballot. If they both pass, the one with the most votes wins.

Really, it shouldn't be all that difficult. The 
arguments against it will really be that it will 
make it easier for third parties, but probably it 
will mostly serve to prevent the spoiler effect 
from being as common a danger as it presently is.

And it will open the door to Range, being an 
obvious next step. Which might be Range 3 or Range 10 rather than Range 100.