On Wed, Nov 13, 2002 at 12:54:59PM -0500, Branden Robinson wrote:
> > Definition: An option F is in the beat path of option G if
> > option G defeats option F or if there is some other option
> > H where option H is in the beat path of G AND option F is in
> > the beat path of H.
> I'm not crazy about recursive definitions.
> Definition: An option F is in the beat path of option G if option G
> defeats option F, or if there is another option H which defeats G, AND
> option F defeats H.
This isn't equivalent.
First, it's wrong: G defeats H and H defeats F, for F to be in the beat
path of G. I really dislike the phrase "in the beat path of", since it
makes exactly this sort of mistake easy to make. Please let us switch
to "transitively beats" or "dominates" or something with a similarly
intuitive meaning.
Slightly more subtly, though, it's not equivalent: if you've got A
defeats B, B defeats C, C defeats D, (and C defeats A, D defeats A,
and D defeats B), then D is still in the beat path of A, even though
neither of the following are true:
B defeats D and A defeats B (F=D, G=A, H=B -- B doesn't defeat D)
C defeats D and A defeats C (F=D, G=A, H=C -- C doesn't defeat D)
This is possible in an election where people vote as follows:
50 DABC
40 BCDA
30 CDAB
A defeats B, 80 to 40
B defeats C, 90 to 30
C defeats D, 70 to 50
C defeats A, 70 to 50
D defeats A, 120 to 0
D defeats B, 80 to 40
> With this definition you can mentally "build up" a beat path,
If you want to avoid recursion, you need explicit iteration, something
like:
Option F is said to transitively beat option G if F beats G, or if
there are a sequence of options, H_1, H_2, ..., H_n, such that F
beats H_1, H_i beats H_i+1, and H_n beats G.
> I suggest this because, being American and thus unaccustomed to
> preferential voting mechanisms, I was unfamiliar with the concept of
> "beat path" when I was first exposed to it.
"beat paths" are exclusive to Condorcet style voting, and Debian's still
the sole group to actually use one of those, outside of election-method
geeks. So it ain't just yankees who aren't familiar with it.
Cheers,
aj
--
Anthony Towns <[EMAIL PROTECTED]> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.
``If you don't do it now, you'll be one year older when you do.''
