[EM] Brief comments on FBC definitions

[MIKE OSSIPOFF]

I noticed some time ago that Craig Carey was still saying that
I never defined FBC. That topic was thoroughly discussed long before,
at which time I finally had to stop taking the time to reply to
Craig's 27K postings.

But, since it's brief, let me repeat that definition here:

Favorite Betrayal Criterion (FBC):

By voting another candidate over his/her favorite, a voter should
never gain an outcome that s/he prefers to every outcome that s/he
could get without doing so.

[end of definition]

What I mean by voting one candidate over another:

A voter votes A over B if s/he votes in such a way that one could
contrive some configuration of other people's votes such that,
if we delete from the ballots every candidate but A & B, A is
the unique winner if & only if we count that voter's ballot.

[end of definition]

I suppose one could add to that "...and no one can contrive a
configuration of other people's votes such that, if we delete from
the ballots every candidate but A & B, the unique winner is B if
& only if we count that voter's ballot."

I don't think that addition is necessary, but it could be added
if someone devised a reasonable example where it seemed necessary.

Or maybe just say that, if when we've deleted from the ballots every
candidate except A & B, if that voter's ballot changes the outcome,
it will do so only by making A the unique winner, or making B not
be the unique winner.

Forest has written a more generally-applicable, but more complicated
FBC. It applies in some special situations where my definition doesn't
apply. As Crag Carey pointed out, my FBC definition doesn't say anything
about situations where someone has more than one equally favorite
candidate, for example. Both FBC versions are useful. My FBC makes
the distinction that I wanted to make, though it doesn't apply in
all situations, and it's brief & simple enough to use in public
discussion. Of course something more universally-applicable can be
useful in mathematical discussion.

Mike Ossipoff



_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp