Lying about FBC

[Alex Small]

Craig-

Since you didn't request that I keep your message private, and since you
seem to enjoy reading the list and issuing patronizing comments concerning
posts, I might as well make public this discussion of my posts.  If you
wish for me to keep your message private, please say so in the future and
I will honor the request.  Here's my response:

Craig Carey said:
> "You have to consider the possibility that favorite betrayal
>  gives the same result"
>
> That is in the paragraph where you equate the alteration of a single
> ballot paper with a perfectly undefined thing of Ossipoff that
> tests all methods without the number of winners, candidates, or
> papers ever being defined.

The number of winners is specified to be one, and in every post I've
stressed that the result only applies to races with 3 candidates.  If I
failed to mention that in each and every sentence, so that some sentences
might seem to be lying when taken out of context, well, by that absurd
criterion I guess I'm guilty, and you can put me on the same list as Bill
Clinton.  The number of voters was either an arbitrary positive integer or
an arbitrary odd number (hence I would say "m voters in this category, m
in another category, and 1 in the third category", giving an odd number
2m+1).

The word "possibility" does not invalidate any of the results I've
presented as proofs.  Those proofs may, of course, contain fallacies that
I have not yet rooted out, but the word "possibility" was used to discuss
a case where I have not presented any proofs:  Methods that satisfy the
majoritarian criterion but not monotonicity.  My result concerning
Condorcet methods addresses a subset of non-monotonic and majoritarian
methods, but not all nonmonotonic and majoritarian methods.

There's nothing wrong with using the word "possibilities" when discussing
a proposition that has not yet been proven true or false.  The task is to
take that proposition and establish whether it is true or false.  Until
that task is accomplished, there are things that we don't know, hence the
word "Possibilities."

> Don't forget that Mike Ossipoff resplied to
> my request for the definition of the "favorite" by saying that
> it was what I wanted it to be, rather than, say what you or your
> fellow student, Mr Ossipoff, wanted it to be.

Kindly refresh my memory.  I thought a favorite is the candidate whom you
prefer over all other candidates in that election.  If you've found a
different definition, maybe you should join Bill Clinton on the list of
people who abuse definitions of words.

> Do you believe that the HOTMAIL.COM person's FAVORITE BETRAYAL
> notion, is somehow important enough to be something that should
> ever be mentioned ?.

Ah, so the quality of a person is judged by his choice of e-mail services.
 I see.  Glad we got that straightened out.  I no longer have to read and
evaluate what Mike says, because his e-mail address is far less impressive
than yours.

And, irrespective of Mike's choice of e-mail service providers, the
question of whether you can design a voting method that gives special
status to your favorite is a fascinating one.  Gibbard and Satterthwaite
proved that onto and nondictatorial voting methods are always manipulable
(i.e. there are cases where a single person voting insincerely will elect
a candidate whom that the person in question prefers to the candidate
elected if that person votes sincerely).

However, some voting methods give more incentives for insincere voting,
while others give fewer.  Gibbard and Satterthwaite's theorem doesn't
address whether incentives for a particular type of insincere voting could
be eliminated.  I've proven that for particular categories of voting
methods (monotonic and majoritarian, and Condorcet), it is impossible to
eliminate all incentives for insincerely ranking another candidate ahead
of your favorite.  The result is far less general than that of Gibbard and
Satterthwaite, in that it applies to fewer voting systems, but it is
interesting and yields more information than their result for the voting
systems under consideration.

> I put the word lying in the title to match up with my belief of
> the truthfulness of your comment implying you know that Condorcet
> is failed by the preferential voting testing Boolean valued
> function named the Ossipoff Favorite Betrayal "criteria":
>   "I know that Condorcet methods don't,

Craig, as much as I enjoyed this message, if you don't come up with some
better objection I'll probably just ignore you next time, and you'll have
to soothe your ego by critiquing another person.  Is there someone else
out there you can talk to?  No!  Now go, or I will taunt you a second
time!  ("This is your last chance.  I've more been than reasonable..."
then a cow flies over the wall).

Sorry, couldn't resist the Monty Python reference...  ;)


Alex


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