[EM] SARC definition improvement

[MIKE OSSIPOFF]

Markus quoted me:

>you wrote (16 Sep 2000):
> > I asked you if you agree or disagree with my claim about
> > what it means to say that a method complies with a
> > criterion that refers to some candidates by letter
> > designations and speaks of a way of voting that's
> > available to certain voters. You haven't answered
> > whether or not you agree with my claim about what that
> > means. I asked you, if you don't believe it means what
> > I say it means, then what do you think it means to
> > say that a method complies with such a criterion?
> > You haven't answered that either. You claim that the
> > criteria are ambiguious, but you don't know what
> > you think it means to say that a method complies
> > with such a criterion.
>

Markus said:

>Suppose someone says: "If every voter strictly prefers
>candidate A to candidate B then candidate B must not be
>elected."

That sounds like a popular mis-statement of Pareto. It's also
close to UUCC, except that instead of saying that B can't win,
UUCC says there shouldn't be a situation where voters will feel
strategically compelled to keep voting in the way that's making
B win. (I stated UUCC more precisely in a posting a few days or
a week ago).

The above criterion is unmeetable. UUCC is met at least by
Approval.

>How would you interpret this requirement? To
>fulfill this requirement, is it necessary that the
>statement above is met for each pair of two candidates
>simultaneously?

No.

>Or is it sufficient that the statement
>above is met for just one pair of candidates?

One at a time.
Any one ordered pair of candidates whom we choose from
among the candidates in the example being considered. For any ordered
pair we choose as A & B, the criterion's requirement must be
met for that ordererd pair.

But, as you suggest in your next question, there seems to be
an ambiguity.

>Or is the
>requirement ambiguous?

Well, maybe, because it isn't entirely obvious to me, right away,
what an example for using this criterion would consist of.

We could say that an example is a configuration of everyone's
sincere preferences, or a configuration of everyone's votes.

Obviously, with either kind of example, the criterion would
be unmeetable.

That shows that sometimes it's necessary to specify what an
example consists of. This criterion should specify something like,

"For any configuration of everyone's sincere preferences [or
everyone's votes] that we consider..."

If we knew what an example should consist of, then,
in accordance with my claim, posted yesterday, your criterion
means:

With every example that we consider, no matter which candidate in
the example we take as the "A" referred to in the criterion, and
no matter which candidate we take as the "B" referred to in the
criterion, if everyone prefers A to B, then B shouldn't win.

I've just realized that my claim about what it means for a method
to meet a criterion that names candidates with letters isn't
useful for WDSC & SDSC, because for whichever (A,B) we're using,
from the example's candidates, the majority preferring A to B
(if one exists) must not have their votes specified in the
example, because we're only talking about those voters having
a certain kind of way to vote, but everyone else's votes must
be specified. So if we're using one example, and taking every
possible (A,B) from that example's candidates, then the problem
that Markus referred to seems to exist: The votes that are
specified & not specified are different depending on which
candidates in the example are considered A & B. And a single
example can only have certain votes specified & certain ones
not specified.

So I owe Markus an apology, for when I said that his ambiguity
argument was wasting time. But right now I don't believe that
WDSC & SDSC need added clarifying wording. It seems to me that
all that needs rewording is my claim about what it means to meet
a criterion that names candidates by letters. I shouldn't have
said that A's & B's are chosen from among an example's candidates.

I should have said that a method meets a criterion that names
candidates by letters if the criterion's requirement is met for
every example consisting of a candidate A, a candidate B,...
[as many as the criterion names], and any other candidates
that we choose to add.

In the specific case of WDSC, the criterion refers to candidates
A & B, and talks about the kind of way of voting that must be
available to a majority preferring A to B (if there is one).

A criterion like that calls for an example consisting of a
candidate A, a candidate B, with a majority preferring A to B,
and some configuration of the other people's votes--any
configuration of the other people's votes.

I claim that it isn't necessary for WDSC's wording to say what
kind of example it uses, in what kind of a configuration we look
for a failure, because it seems clear that WDSC calls for an
A, a B, a majority preferring A to B, and says that the requirement
must be met for that majority. Saying nothing about the other
voters, the criterion requires that a method be tested with any
configuration of the other people's votes that anyone suggests
that we try, in order to find a failure. So then, I claim that
WDSC calls for the kind of example described in the previous
paragraph, and so WDSC doesn't need added wording to specify
in what kind of configurations we look for a failure.

I don't think Markus's ambiguity problem remains if compliance
with a criterion that names candidates by letters means what
I said above in this letter--what I said today, not yesterday.
That's a plausible meaning, and makes more sense and is more
flexible than what I said yesterday.

Markus can still disagree with today's meaning for compliance with
a criterion that names some candidates by letter designations, but
I think my meaning is plausible, better than yesterday's, and
is something that people would agree with.

If Markus says that, for WDSC or SDSC compliance, the criterion's
requirement must be met simultaneously for every ordered pair
of candidates in the example that we take as the A & B referred
to by the criterion, then, for one thing I think that doesn't
agree with the obvious interpretation of the criterion. I claim
that my (today's) version of what it means to meet a criterion
that names candidates with letters is instead what people would
agree with.

Also, if Markus wants to say that the criterion's requirement
should have to be met for every ordered pair that we take as the
A & B referred to in the criterion, then he must write his
complete claimed meaning for what it takes to meet a criterion
that names candidates by letter designations. I've asked Markus
what he thinks it means to meet such a criterion, and he hasn't
answered. If he doesn't have a meaning for that, then my
meaning is uncontested, and WDSC & SDSC have no ambiguity
problem. I don't know if it's even possible to write a meaning
for compliance with a criterion that names candidates with
letters, so that the criterion's requirement must be met by every
ordered pair of candidates in the example we take as A & B, without
contradictions or inconsistencies. In any case, Markus hasn't
written such a suggested meaning.

UUCC carefully specifies what in what kind of a configuration we
look for failures, and SFC & GSFC talk about a majority who
_votes_ one candidate over another, and so I don't expect
there to be the amount of discussion needed for those. But
if someone shows that those criteria have a question that
needs as much answering that Markus' objection to WDSC & SDSC
needed, then I'd be glad to discuss those also.

And anytime anyone shows that one of my criteria needs more
clarifying wording, I'm glad to add it. Otherwise I try to keep
them as brief as possible, leaving out anything that is
implied in the briefer wording. I still claim that WDSC & SDSC
are complete as-is, and work fine if we use the most obvious
& agreed-upon meaning of compliance for criteria that name
candidates by letters.

And, Markus, if you don't agree with my claim (today's) about
what it means to meet a criterion that names some candidates
with letter designations, than what do you think it means to
meet such a criterion?

Mike Ossipoff





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