[EM] Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 11:35 PM 11/7/2006, Michael Poole wrote:
>The original claim is "Approval does not satisfy the Majority
>Criterion".  If you redefine either Approval or Majority Criterion
>such that you can accurately say "Approval-prime satisfies the
>Majority Criterion" or "Approval satisfies the Majority-prime
>Criterion" it is distinct from the original claim.

It is unnecessary to revise either Approval Voting or the Majority 
Criterion. As written, AV satisfies the MC, and the arguments I see 
on this, so far, do not really address the issue. Show me a proof 
that AV does not satisfy the MC, but Plurality does.

To do so, you must define "strictly prefer." Approval allows only one 
expression of strict preference, that which is in the MC. It *also* 
allows abstinence from expression of preference, which is also true 
of Plurality.

However, with Plurality, one may multiply-vote No, it is only 
multiply-voting Yes which is prohibited. Thus Plurality does not 
raise the issue that I've raised.

The issue is that an Election Criterion cannot be objectively applied 
based on the state of mind of the voter. If a majority of voters 
express a "strict preference" of one candidate over all others, that 
candidate cannot fail to win, under Approval or Plurality.

That Approval allows voters to do something else, which is to abstain 
from expressing a strict preference between sets of voters, this does 
not change the fact. These voters, who have elected to use Approval 
in this way, have abstained from indicating the "strict preference" 
which is part of the Criterion, and therefore they are not party of 
the "majority."

Now, it does appear to me that the people who have explained the MC 
in the past have been to some extent aware of the problem, which is 
why we get vague language like "if the voters are asked which 
candidate they prefer over all the others," "Asked?" How? It must be 
on the ballot, and it must be through a method of expressing such 
strict preference that the ballot allows. Approval allows such 
expression. In only one way. Exactly the same as in Plurality.

Look, this is airtight. I'm not stupid. Ditzy, sometimes, but not 
stupid. It has happened that I've been utterly convinced of 
something, with this level of certainty, and I've been wrong. But it 
does not happen often, and *nobody* has answered this argument so 
far. Instead, we get irrelevancies, such as:

> > Now, it is possible for voters to answer the question posed in the MC,
> > using an Approval ballot. Same as a plurality ballot. Simply vote for
> > the candidate preferred and for no others.
>
>Yes, but that is not how Approval is defined to work.

Huh? Approval is defined how? It appears that we have some kind of 
method definition which has no effect on how the ballot is designed 
and counted. The ballot is designed exactly as a plurality ballot, 
only the rule that tosses overvoted ballots has been made inactive.

I'm sure that Approval Voting is defined in some ways and in some 
places by how the designers think voters should vote. But I would 
prefer, strongly, to consider a one-to-one relationship between 
"election method" and the design of the ballot and a method of 
counting or otherwise determining the result from the ballot. If two 
allegedly different methods use the same ballot and the same method 
of counting, they are the same method, period. Possibly with 
different strategies.

In any case, I'm arguing that Approval should be promoted as a simple 
change to the election code, and the argument that people should vote 
for more than one should probably not be a lead argument. That 
Approval will eliminate the spoiler effect, maybe, maybe not. 
Discarding overvotes is unjust and is actually a contradiction in the 
law in states which require that a vote be counted if the intention 
of the voter is clear. That is, in Florida 2000, a large number of 
overvotes for Gore and Buchanan were discarded. But the Buchanan 
votes were irrelevant to the outcome, and these voters had clearly 
expressed a preference for Gore over Bush.

Yes, because the code expressly says what to do with overvotes, this 
overrides the common-law argument. But strike that provision, I think 
it is possible that a court would order counting all the votes. 
Indeed, this should be our slogan:

Count All the Votes!

Slogans of

Help Third Parties Grow!

or

Vote for More than One

are not going to fly, even if implementing Approval would actually allow this.

These are arguments for Approval, they are not part of the method 
itself. Except for the first one. Count all the Votes!

>   "Approval voted
>according to Plurality satisfies Majority Criterion" is true but not
>useful because it is the same method as Plurality.

I never said "Approval Voted acording to Plurality." Rather, I said 
that Approval has exactly the same method of expressing "strict 
preference" as Plurality. Other voters may do something different, so 
the method is different. Some have voted as they would vote under 
Plurality and some may vote differently.

And if a majority votes exclusively for one candidate, which is the 
only meaning I can assign to "strict preference," under Approval, 
that candidate cannot fail to win.

>   "Approval
>satisfies Majority Criterion" is false because Approval permits voters
>to approve of more than one candidate.

It permits it but does not require it. Plurality also permits a 
majority to divide its vote, such that there is no majority 
candidate. Does this mean that Plurality does not satisfy the MC?

*If a set of voters meets the definition in the Criterion, then the 
condition required by the Criterion must be true." Isn't this how we 
apply such a voting criterion?

>Strict preference means that equivalence is excluded but it does not
>address magnitude.  "Strictly prefer X to Y" means, in preference
>terms, "X > Y" rather than "X >= Y".  This is basic set theory.

That's right. "equivalence is excluded." If a set of voters do not 
provide equivalence information, but indicate only "strict 
preference," there is no expression of magnitude, there is only preference.

>It is not accurate or honest to ignore voter preference or treat it as
>irrelevant when the ballot does not allow it to be expressed!

Does Plurality allow the expression of preference? How?

Approval allows the same expression. That it permits but does not 
require voters to do something else is irrelevant. Voters can also 
express a preference and then scribble on the ballot, or violate some 
other rule, such as writing their name on the ballot, causing it to 
be discarded. Does this cause a method otherwise satisfying the 
Criterion to no longer satisfy it? Obviously not!

If a majority express a strict preference, using an Approval ballot, 
which Approval allows them to do, that candidate cannot fail to win. 
Isn't this clear?

If it is not, well, the election methods community is out to lunch. I 
don't think it is. I'm looking

>Translating the logical flaw to a different metric: Strength of
>preference is not expressed on a simply ranked ballot.

That's correct. Why does this writer think it necessary to explain this?

>Also, could you please try to edit your posts down?

Tell you what. If they are too long for you, don't read them. Nobody 
is holding your nose to your computer.

>The Condorcet Winner is a candidate who, for every other candidate, is
>(strictly) preferred by a majority of voters over the other.  If the
>CW is not acceptable to a majority of voters, then there *is no*
>candidate that is acceptable to a majority -- otherwise that same
>majority would prefer that candidate over the CW, which violates the
>definition of CW.

This makes a very important and false assumption, which is that in a 
runoff election following any election method, the voters will vote 
according to the same preferences as they voted in the original 
election. I have seen the direct opposite happen in a situation where 
Approval information existed regarding the choices. G?uess what? A 
strong majority would rather have a broadly acceptable winner than 
one who is merely their weak preference.

Further, the question being asked in a Ratification election (which 
is different from a Runoff) is "Shall *this* candidate be elected." 
It is a different question than "Do you prefer this candidate to all 
others." It takes into account preference strength, for the real 
question is, "Shall we hold another election or shall we accept this 
winner?" Strong preference, vote No. Weak preference, vote Yes. You 
decide what is strong or weak. You decide which is worse, delay in 
completing an election or the election of a particular candidate.

This is actually quite simple. Suppose that there is a Condorcet 
winner, but this victory is produced by equating weak preference with 
strong preference, which Condorcet methods necessarily do. In a 
ratification election, voters may well say, "It is not worth the 
trouble of holding another election, since this other winner -- say 
the Range winner -- is quite good enough. Not my first choice, but 
almost as good. Indeed, I'll be *happy* with this outcome."