[EM] 06/24/02 - The 'true majority winner'

[Alex Small]

At the risk of misrepresenting Mr. Hager's intent, I think I can elucidate
from his post what he meant by "true majority winner."
> "The advantage of AV over other systems is that it is very simple, very
> good at finding the true majority candidate, and would cost essentially
> nothing to implement.  I know of no other system which has all three

Here's the first use of the term "true majority winner."  He says that
Approval is good at finding it, but he does not say that Approval _always_
finds it.  My doctor is good at curing diseases, but he doesn't always
succeed at curing diseases.
The post doesn't suggest that the Approval winner is by definition the
"true majority winner," but that the "true majority winner" and the
Approval winner often coincide.
> The best ranked system, incidentally, is not IRV -- it's called the
> Condorcet method.  In voting science, Condorcet is the standard by
> which all other voting methods are measured.  In fact, the term voting
> theorists use for the majority winner is the "Condorcet winner" because
> Condorcet will always find the true majority winner in an election.

Here Mr. Hager seems to explicitly state that he uses the term "true
majority winner" to denote the Condorcet winner.  We can, of course,
debate whether the term "true majority winner" is an accurate description
of the CW, but Mr. Hager's intent seems clear.
My only objection is to the use of the word "always":  Condorcet only
describes half of an election method:  The half that finds a winner when
somebody wins all pairwise comparisons.  The other half of any method in
the Condorcet family is a procedure for resolving cyclic ambiguities. 
Perhaps he should have stated "Condorcet will always find the true
majority winner in an election, provided that there is one."
> unlike Condorcet, IRV will often fail to find the true majority
> candidate."

I've excerpted this from a longer comment.  The context is a criticism of
IRV.  We can debate whether failing to elect the CW is a serious flaw of
an election-method, but the statement that IRV can fail to elect the CW is
true.  Perhaps the word "often" needs a little clarification, of course.
Does this resolve questions over interpreting Mr. Hager's post? 
Clarifications from Mr. Hager or those who have corresponded with him are
obviously welcome.
Alex Small

-- 
The first thing we do, let's kill all the lawyers!

Of course, that's just my opinion.  I could be wrong.


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