2 Criteria

[Mike Ositoff]

Some time ago, Demorep asked about how many criteria there, and
Markus mentioned 6 main ones. 

It seems to me that 2 are essential: 

Condorcet & GMC

or, better, Smith & GMC

or probably better still, Smith & Beat-Path GMC

***

Meeting one of those pairs of criteria seems the important thing,
for complying with standards important to so many people.

***

Markus's Beat-Path GMC seems better than ordinary GMC, by not
requiring the disqualification of a subcycle with a cyclic majority
(as long as the subcycle is a clone-set). Sometimes the members
of consist of at least one winner with respect to the altenatives
outside the subcycle. As I've said, I consider that "fine-tuning",
improvement on something that certainly is far from inadequate.

Another advantage of Beat-Path GMC over ordinary GMC is a neater
definition. I've decided that a good way to say ordinary GMC is:

Never avoidably elect an alternative that has another alternative
ranked over it by a majority.

But avoidably means 2 different things, under different conditions:
When we're not using the Smith set, and consider all the alternatives
to be candidates without separating some out before applying a
choice rule, then, for electing a majority-beaten alternative to
be unavoidable, every alternative would have to be majority-beaten.

But if we've agreed that it's important or preferable to only
choose from the Smith set, and that's our first rule, then of
course electing a majority-beaten alternative would be unavoidable
if everything in the Smith set is majority-beaten.

As Markus pointed out, Beat-Path GMC avoids that little inelegance
of a word with 2 meanings in 2 situations.

Of course Beat-Path GMC relates to Schulze's method as
ordinary GMC relates to Condorcet(EM). Markus has advanced
methods & criteria a notch, and now may well hold the prize for
the best simple method (A "simple method", as I use the term,
is a method using only 1 balloting, and whose only input is a
ranking or set of point assignments from each voter--technically,
refinements or improvements like candidate withdrawals seem to
me to be additional input to the election's final choice).
I don't know if some of the iterative methods we were dicussing
earlier would be better than Schulze's method. Maybe not, because
they don't give us compliance with an additional criterion. 
Their more complicated procedure could make offensive strategy
even more difficult, but none of our iterative methods manifested
that advantage with the 4-candidate example that I tested them on.

But as I was saying, Smith//Condorcet(EM) & GMC might be easier to
explain or define relatively quickly.

***

Compliance with either version of GMC gives automatic compliance
with Pareto, it seems to me.

Compliance with Condorcet automatically gives compliance with Majority.

Compliance with Smith automatically gives compliance with
Condorcet, Condorcet Loser, Majority Loser, and Mutual Majority.
(and maybe with other similar criteria).

Because those criteria give compliance with other criteria, and
because some additional important criteria are too obvious to
have to mention--that's why I say one of those pairs of criteria
that began this letter would be enough.

***

One criterion that is an example of a criterion that's too
obvious to mention is the No Dictatorship Criterion. Actually,
unless CVD's way of making choices has changed since I was a
member, CVD's choice procedure probably violates No Dictatorship.

But CVD can proudly point to the fact that it's choice procedure
(barely but reliably) meets Pareto :-)

***

Of course violation of No Dictatorship is a more extreme form of
violation of the stronger Anonymity Criterion. Anonymity says
that all voters should be treated the same by the method.

Anonymity is important, because it's a much better expressed way
of saying what the regrettable "1-Person-1-Vote" is trying to say.

Of course, if the members aren't voters in the 1st place, then
maybe it's unfair to say that CVD violates No Dictatorship or
Anonymity. :-)

Otherwise, would it be No Dictatorship, or just Anonymity that
is violated? I don't have enough details about the organization
to say for sure, but I suspect that the No Dictatorship Criterion
is the one violated, if member opinions were counted as votes,
and if the orgznization is as it was or seemed to be when I was
a member.

Mike Ossipoff