Reply: Bruce's incorrect statement
dfb at bbs.cruzio.com
Thu Nov 7 12:30:51 PST 1996
I stand by my claim that Bruce's statement was false. The whole
justification for the statement was exact precision, but if his
statement is taken literally, then all of the wordings make the
assumption that he describes. Oh yeah? What about wording #1?
If you have no losses, then you have zero votes against you in
So Bruce's statement that those wordings make the assumption that
he says they make is false, since not all of them do.
Admittedly, wording #4 would require more words added to make
it sufficiently precise for publication in a mathematical journal.
But anything added to make it that precise will add a sentence,
or a clause that will complicate an existing sentence. And all for
the purpose of convering a situation that's irrelevant to public
elections. Besides, in addition to complicating the sentence itself,
or adding one, it would also bring up an issue that we needn't lay
on the person-on-the-street. We don't have to talk to them about the
distinction between beating everyone & being unbeaten, or about
the consequences of pairwise ties, even by implication. The clause,
if added, would raise questions, would make the person feel they
don't understand the method.
That being said, I want to add that I'm not _staunchy_ opposed to
adding a short sentence or clause to make #4, or perhaps #2 or #3 if
needed, more precise, as long as it can be done without adding too
much complication, structurally & conceptually, intruducing the
reader to questions that aren't relevant to public elections.
Especially if there's a neat way of doing it without adding a
sentence or clause, but by just changing something without
lengthening it. But, while not staunchly opposing it, I personally
don't consider it necessary, and, if it adds a clause or sentence,
or if it makes the reader start worrying about an issue irrelevant
to public elections, then I suggest that it isn't desirable.
For legal language, obviously I agree that precision is always more
important than brevity! Certainly the legal language must be made
And if #4 is presented after #1, #1 already covers the situation
Bruce is concerned about anyway, though #4 remains imprecise.
(In my copy of this message, some sentences are scrambled or
repeated. I hope that doesn't happen in your copy)
Being unbeaten, as the method has been defined, results in a zero
Condorcet score, just like beating everything else. That's ok, since
the job for which Condorcet's method was chosen had to do with
comparing defeats, detecting majorities-against.
It's because Condorcet ignores whether an unbeaten alternative beats
anything that I propose Beat-Something as the 1st tie-breaker,
_in small committee elections where people agree that they want
to do an ideal count_ It's the kind of refinement that might go with
using the Schwartz set instead of the Smith set. I've indicated that
if EM were going to take a vote, and the tie-breaker(s) were not
yet established, then I'd quickly agree to whichever tie-breaker(s)
anyone proposed, rather than delay the vote, since I don't
consider tie-breakers important. The importance of Beat-Something
is reallly only aesthetic, since Condorcet does its job completely
even when it returns a tie, whether the equal Condorcet scores
result from 2 unbeaten alternatives or not.
But of course if we were to design the method in advance, instead
of discussing it when a vote was needed immediately, then I'd
suggest using the Schwartz set, and using Beat-Something, Fishburn,
& Stepwise-Plurality as tie-breakers. Though I consider plailn Condorcet
ok, the fact that even 1 person on EM hates it, &/or the fact that
several would prefer using Smith or Schwartz, is enough reason
to use Smith or Schwartz. Without pairwise ties, the Schwartz set
is identical to the Smith set. If there are pairwise ties, Schwartz
is more exclusive. It excludes a Smith-set member who is beaten
from within the Smith set but beats nothing in it.
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