[EM] Query for Approval advocates

[Bart Ingles]

Eric Gorr wrote:
> 
> At 11:49 PM -0700 8/20/03, Bart Ingles wrote:
> >Why should it be considered important to find a majority when none
> >exists?  In my view, the very concept of 'majority' is meaningless when
> >there are three or more candidates, and appears to be based on several
> >logical fallacies including:
> >
> >(1) Round number fallacy:  The 50% figure is viewed as magical because
> >it has the appearance of being a "natural" threshold.  Which it is--if
> >there are only two candidates.
> 
> It is a natural threshold regardless of the number of candidates.
> If > 50% of the population desire a certain option, that option
> should be selected despite of the number of other options out there.

True, if and only if you're talking about the voters' first preferences
on the ballot.  This is akin to Pareto, in that it is sort of a
common-sense minimum requirement.  But it doesn't seem all that useful,
since so many methods pass this requirement, including Approval,
Bucklin, Condorcet, FPTP, IRV, Runoff, etc.  The only ranked ballot
method I can think of that fails is Borda.  And I guess Cardinal Ratings
fails.

This particular kind of majority is not sufficient to define a voting
system, since (a) you cannot guarantee that any candidate will have a
1st choice majority, and (b) if equal-ranking is allowed, you can have
multiple candidates with a 1st choice majority.  Nor is it necessary,
unless you have a "None of the Above" rule.  But this is the type of
majority often falsely equated with other "majorities" when committing
the equivocation fallacy.


> >(2) Circular reasoning:  Majority proponents generally have a particular
> >method in mind for arriving at a "majority".  This method is favored
> >because it produces a majority, but the majority is defined in terms of
> >the method.
> 
> This seems to be false as well.
> 
> Take this example:
> 
>    40:A
>    35:C>B
>    30:B

The above contains a Condorcet cycle.  I assume you intended for B to be
the Condorcet winner, so for sake of argument I will substitute the
following:

40:A
30:C>B
35:B

> That I believe B should win, is independent of any particular method.
> Why should B win?
> Because it is obviously preferred by a majority of people over every
> other option.

Technically false: only 35 of the 105 prefer B over every other option. 
In the example, a majority prefer B to A, and a different majority
prefer B to C.

You could say that "B is obviously preferred by *majorities* of people
over every other option, but even so the "majorities" are merely
incidental.  B would be the CW without them:

40: A
10: C>B
20: C
35: B>A

Here B is preferred by *pluralities* of people over every other option,
but is still the CW.

> Now, the fact that I can point to a method that will select B is a
> reason why I would prefer that method to a method that would select
> something other then B.

So do you still think the CW should win in the immediately preceding
example?  If so, your belief must be based on something other than
majority, since the only majority above is the 75:30 majority which
prefer A to C.


> >(3) Equivocation:  The majority produced by a particular method is often
> >touted as though it were equivalent to an outright majority of
> >first-choice votes.
> 
> No, I would not say equivalent, but it is close enough that in the
> case above, the difference between equivalence and something else is,
> at best, elusive.

I'm not sure what this means.  What the hell, apples and oranges are all
fruit?


> >But it would be easy to make a case that a
> >candidate with a 49% plurality (or 45% or even 40%) really enjoys more
> >public support in a 3-way race than someone with only 26% of
> >first-choice votes and a similar number of 2nd-choice votes.
> 
> Ok, so you have an option where 49% of the population marks A first.
> 26% of the population marks B first.  However, we cannot stop there
> as we have not accounted for the other 25% of the voters.  If all 25%
> prefer B over A, why should B not win?

Depending on where you stand on the social welfare function vs. cardinal
utilities debate, maybe B should win, maybe B shouldn't.  Either way,
the term 'majority' has no part in any valid justification.

Bart