[EM] Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 06:31 PM 11/8/2006, Michael Poole wrote:
>Abd ul-Rahman Lomax writes:
>
>[snip]
> > 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.
>[snip]
>
>Coming from someone who recently advocated in favor of exit polls as a
>way of measuring actual voter preference, this insistence on looking
>only at ballot markings is extremely strange.

This is getting entirely out of hand. Exit polls may be useful for 
this or that, but they are irrelevant when it comes to whether the 
election method being used satisfies one of the election criteria.

I'm saying that *for evaluating an election method objectively,* we 
must look only at the ballots, not at what people say about them, 
urge voters to do with them, or think about the candidates.

The criterion says that "if a majority of voters do X," -- and it 
must be interpreted that way, rather than "if a majority of voters 
think X," since people often do not do what they think, for various 
reasons -- and Y must happen if they do this, then the method 
satisfies the criterion.

Voters can do X with Approval Voting, just as they can, and in the 
same manner, as they can do it with Plurality. That they cannot 
simultaneously do X *and* do something else which Approval allows but 
does not require, and which Plurality prohibits on pain of discard of 
the ballot, is irrelevant.

If they do Y, then, as it happens, they have not done X. So? They are 
not required by the method to do Y, it's an option.

Approval voters may express exclusive preference for a single 
candidate, just as they can in Plurality, and in the same manner. If 
a majority of them do that, then this candidate must win. That these 
voters have additional options does not change this in the least, and 
every other voter in the election, if a majority have expressed 
strict preference for a candidate, can do whatever they like, the 
majority-preferred candidate must win.

>   The winner contemplated
>under MC has never been, and should not be, defined by what the ballot
>allows a voter to express.

This is utter nonsense. If the ballot allows the voter to express 
what the criterion is using as a standard, then the criterion can 
directly evaluate the method. We can also say that the criterion is 
not satisfied -- the usual language -- if the method does not allow 
expression of the necessary data. Thus a Condorcet method, to fully 
satisfy the Condorcet Criterion, must allow all candidates to be 
ranked. However, the number of ranks expressable could be truncated; 
and, while the method would not strictly satisfy the criterion, since 
it would be possible to postulate an election situation where voters 
could not provide the necessary data, we could state that it 
sufficiently or generally satisfies it.

>As an extreme case, in an election for president with three
>candidates, if the ballots only have one checkbox, and the name of
>George W. Bush next to it, does that make Bush the majority winner?

Yes, probably. There is, in this election, only one candidate. For 
election method analysis, candidates not on the ballot are not 
considered, unless they may be added by the voter and thus counted in 
the same way as would be candidates on the ballot.

What is happening here is that we are seeing a series of arguments 
that are so silly that they must be coming from a fixed opinion to 
which the writers are attached, though it is possible that they are 
playing the devil's advocate role and attempting to exhaust all 
reasonable or even unreasonable arguments.

>A lot of your other claims are wrong -- for example, claiming that I
>make a "very important and false assumption" about a secondary
>election that I neither considered nor discussed -- but most of them
>boil down to the issue of whether election criteria should be judged
>based on objectively obtainable information or on what the ballots
>actually capture.

"Objectively obtainable information." How? Polls? The voters may lie. 
Whether or not a poll is accurate is generally a subjective judgement 
unless verified by actual vote data. The information being described 
here is unverifiable.

Yes, you could run an Approval election in a manner that could 
reasonably be said to collect this data. That is, you could use a 
full Condorcet ballot, for example, but with an Approval cutoff, and 
the ballot would be counted simply as Approval. This is really, 
however, a modified election method, such as my A+ proposal is a 
modified method. It adds a Favorite designation to the ballot, but 
that designation is not used to determine the winner, it is used for 
other purposes. It gets tricky to determine if A+ satisfies the 
Majority Criterion, because really voters are making two separate 
designations, the one effective in the election, and a favorite 
designation, which is optional (and which can likewise be checked for 
more than one, but we assume that most would not do this.)

Voters might, for example, check the Favorite designation in order to 
move campaign funding to the party of that candidate, even though 
they actually prefer, perhaps slightly, the other candidate whom they 
approved. They prefer the *party*, not the candidate, per se.

So I'd say that extra information collected on the ballot, not used 
in the determination of the winner, is irrelevant to election 
criteria satisfaction.

Again, it is very simple, and these writers are trying to make it complex.

The criterion says that if a majority  of voters do X, and Y 
necessarily results from that, the criterion is necessarily satisfied.

Approval allows a majority of voters to do X, and Y necessarily 
results from that. Geez, Louise, it looks airtight to me!

Approval satisfies the Majority Criterion, the news is coming soon to 
a wiki near you.