On Thu, Nov 14, 2002 at 06:24:14AM +1000, Anthony Towns wrote: > 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 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. Sorry about that. I retract my proposed amendment quoted above. > 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 I see. > > 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. Can we use the term "transitively defeat", and thus leave the term "beat" out of the proposal altogether. This way no one will wonder what an unqualified "beat" is. While your definition smacks of mathematical notation (which scares some people), it does seem the most clear way to express this. > > 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. Wow, be careful saying charitable things about Americans, it might tempt W to start a war with Iraq even earlier, citing "international support". </spiteful political grumbing> -- G. Branden Robinson | Debian GNU/Linux | If ignorance is bliss, branden@debian.org | is omniscience hell? http://people.debian.org/~branden/ |
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