SWC's original task
dfb at bbs.cruzio.com
Fri Apr 19 10:16:48 PDT 1996
We've heard definitions of Pairwise methods, and no doubt we could
debate alternative definitions for that word forever, but I'll bet
that we have a pretty good idea now what the alternative definitions
True, we haven't voted on a definition, and I'm sure that none of
us ever intended to, including me. We can include methods that don't
meet the Condorcet criterion as broad-definition Pairwise methods,
a definition that includes Borda's point system as a Pairwise method.
We could have a specific-definition Pairwise method definition that
excludes methods that don't meet the Condorcet criterion. So there's
no problem there, and there's no argument about how to define it--we
could define both.
The fact that one could come up with not-very-good methods consisting
of Pairwise//Non-Pairwise doesn't mean that such methods aren't Pairwise
methods. For instance Bruce & I both advocate using Plurality or
an extended version of Plurality as the final tie-breaker for the Pairwise
methods that we propose. So surely there's nothing to debate or argue
Similarly, we've all described similar procedures & algorithms for
determining the Smith set (I assume that Bruce's formulese-written
algorith is similar to the others we've written). Though Bruce said
that part of my procedure is vague, but didn't say what's vague about
it, and though he said that another statement I made was a "tautology",
those statements have been dealt with. As for "tautology", there's
more to say about that. I alread pointed out that admitting alternatives
to the Smith set according to how few alternatives beat them is convenient,
so then, so what if it's a tautology. I've found a definition of
"tautology" that says:
"A repetion (especially in the immediate context) of the same word
of phrase, or of the same idea or statement in other words, usually
as a fault of style."
You know, calling my statement a "tautology" is a pretty meaningless
statement, because it shouldn't be surprising if a statement that
could be a definition of the Smith set is used as a test for whether
a particular alternative is a member of the Smith set. I wasn't proposing
my wording as an original definition of something new, but rather as a
way of determining if a particular alternative is a member of the Smith
set. Actually the statement that an alternative is a member of the Smith
set if it beats or ties a member of the Smith set would be called by
Bruce even more of a tautology than the statement to which he applied that
name, since it's more directly related to the definition of the Smith set.
Does that mean we can't use that test either, Bruce?
So, the Smith set determination discussion seems completed, except
that I'd like to ask Bruce to tell us how my statement that he
says is "vague" could have more than 1 meaning, and why a test
that is closely related to the definition of the Smith set shouldn't
be used as a test for membership in the Smith set. But if the recent
past in this list is any indication, don't expect him to answer.
But the point of this letter is that we've covered the topics that
we've been discussing. On the definition of Pairwise & on the
determination of the Smith set, we've stated several ways, closely
related, and have accomplished the goals of those discussions.
I've finished my answers to Bruce's anti-Condorcet paper, and Bruce
has had plenty of time to answer the statements & questions in my
letters. So I'm now suggesting that everything that's going to be
said about that has been said.
So all 3 of those topics have been completed, it seems to me. So
I suggest we get back to the original purpose of the SWC: Our
ultimate goal is to send a FAQ to ER about SW standards & how
well the methods meet the various standards, and also to
send them a recommendation for the best method to offer to the
public, and individual assessments, conclusions & reasons for
voting as we did.
Now, if we let Bruce keep us from those goals with more & more
definition minutiae, then I can guarantee that the SWC will never
accomplish its goals--will never even resume the effort toward those
Bruce & I agree anyway that the definition of "Pairwise" isn't important
since it's better to just name methods by their own specific name. And
before we get too involved in exactly what is the most philosophically
attractive wording for how to determilne the Smith set, ought we not
first determine what methods meet what standards, & what method(s) we
like, and intend to recommend to ER?
So then, my suggestion is that now we return to our original task.
We've already got a lot of SW standards proposed. I'd add 1 more
standard: Candidate Counting (the standard involving how many
alternatives a particular alternative beats &/or is beaten by).
Bruce can, if he wishes, propose each one of the candidate-counting
criteria as separate standards. If not, then we could just add
Candidate Counting as 1 standard. I emphasize that I'm suggesting
Candidate Counting because others consider it important, not because
I do. I don't consider it important.
Surely that completes our list of standards, and now we're ready
to vote on them. One issue is whether to vote, 1 at a time, on what
standard we should evaluate methods by next. I suggest that there's
no reason why 1 vote couldn't order the standards, so we wouldn't
have to vote more times. We could simply use our ranked ballots to
find a winner, and declare that the 1st standard to use. Then use the
same rankings again, with that winner removed, to find the 2nd
standard to use...and so on, removing each winner & applying count
methods to the rankings. Shugart's proposed method, a modification of
the familiar Runoff method, could be used as a count method for ranked
ballots, and so ranked ballots could be counted by Condorcet, Copeland,
& Modified Runoff (Shugart's).
Since we may not all agree on what count method to use, there are
1. (I like this one best, because requires no extra voting)
The EM group, when it was known as the technical list, already
voted on what voting method to use, and we chose Condorcet's
method. Surely we don't have to repeat that vote whenever there's
something to vote on. It's much easier if the method we chose remains
our official method till such time as we change it, by another vote.
That saves us from having to vote on how to vote on standards.
Since Bruce doesn't like plain Condorcet, I have nothing against using
2. Take a vote on what voting method to use for voting on standards.
This is ok if people don't mind an extra election to choose a voting
method. This, it seems to me, is quite unnecessary, since we already
have a voting method that we've chosen, in just such a vote, and
if we were going to change (say) to Copeland, then the proper way
to do that, according to existing accepted procedure, would be
for a Copeland proponent to ask for a new vote on voting systems
for us to use--and, for simplicity, that vote should use the voting
system that we've most recently adopted--Condorcet.
So it seems to me that alternative #2 is unnecessary unless someone
insists that we take a new vote on what voting system to use, and
someone seconds that requrest.
3. Use the Combined-Method, where we could collect the rankings,
count them by all the proposed methods, and then take an Approval
or Plurality vote between the winners by those count methods, to
find a winning standard. We could either repeat this procedure for
picking each next standard to use, or, if only 1 method picked the
standard that won the Approval vote, then we could use that method
to order the standards,as described above.
I'm sure you'll agree that #1 is the quickest & simplest. I suggest
that a brief discussion either adopt #1, or propose & second something
else. It needn't be an actual vote, since a) We've already voted &
chosen Condorcet's method; & b) In such a small group, everyone can
participate in the discussion, and a brief discussion, with a proposal
& a second for the proposal, with no objections to that proposal, is
really just as democratic as a vote, and a lot quicker & simpler.
So that's what I suggest. And I'm making a proposal now, alternative
#1: I propose that, because we've already voted on what voting system
to use, and chosen Condorcet's method, then Condorcet's method remains
out method to use. I therefore propose that we use Smith//Condorcet
to take a vote among the standards, and use the resulting rankings from
that vote to order the standards.
Pick the winning standard by Smith//Condorcet, and then remove that
standard from the list, and use the same set of rankings among the
remaining standards to pick the 2nd standard to use...etc.
So there's a proposal. Is there a second? If so, and there's no objection
(which would force a vote) then that would mean that we could immediately
procede to vote on standards, for the purpose of ordering them to determine
the order in which we will use them to evaluate & compare the methods.
By the way, we have _lots_ of standards in our list of standards.
Very likely we won't all vote for all of them in our rankings. That
means that, as is always the case, there'll be lots of "truncation".
Because Copeland is extremely vulnerale to truncation--a sitting duck
for it, and because Condorcet is invulnerable to it, that's one reason
why Condorcet is a better method for this vote.
Also, I've talked about how Condorcet carries out majority wishes &
finds the universal compromise better than Copeland or other methods.
So then, do we have a second for my proposal to immediately proceed
to a vote on standards, by rank balloting, counted by our officially-
chosen method, Condorcet's method (in its Smith//Condorcet version)?
Is there a second?
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