Buddha Buck <[EMAIL PROTECTED]> writes: > Forest Simmons <[EMAIL PROTECTED]> writes: > > > If I had your definition (of voting method) in your language (formal or > > not), I might be able to give a definition (to your satisfaction) of what > > I consider a voting system to be in the same (or similar) language, so > > that you could, for example, see how Buddha Buck's definition of Approval > > fits into that general framework. > > In private email, Craig complained that I ignored negative, rational, > and transendental vote counts. I replied that I also ignored > algebraic irrational, transfinite, complex and quaternion vote counts > as well -- intentionally.
In an email that was waiting in my inbox as I wrote the above, things seem a little clearer now. Craig is (I -think-) considering voting systems where various ballots can have different weights. In which case, a candidate could receive a negative or even transendental number of votes. My suggestion there is that Approval doesn't apply to that situation. That clarification would also affect my comments below -- I am uncertain of the validity of my logic in the face of arbitrarily weighted ballots, and I am unwilling to revisit my previous arguments at 3:15AM when I have to be at work at 8AM. In the context of unweighted ballots, I believe my proof was valid. > He also made some comment about improperly negating negatives, but I > think that that was a miscommunicaiton error. I suspect that when he > saw me saying A(X) = |v1| + |v2| > A(Y) = |v1| + |v3| so that, by > subtracting |v1| from both sides, I get |v2| > |v3| (and therefore, X > is preferred to Y more than Y is preferred to X), he assumed that |v1| > meant the absolute value of v1. In that case, either v2 > v3 or v3 > > v2 could be true, depending on the signs and magnitudes of v2 and v3. > > But since v2 and v3 were defined sets, the standard notation |v2| means (to > me) the cardinality of the set v2, and likewise for v3. In that case, > it makes no sence to discuss v2 > v3 or vice-versa, because v2 and v3 > aren't comparable by >. > > > > > We're having trouble communicating, and we don't want to take a chance of > > some good ideas being lost because of that :-) > > > > Forest
