[EM] More falsity: Concavity is what we want, better that than , a triangle
bmbuck at 14850.com
Thu Sep 27 22:35:22 PDT 2001
Forest Simmons <fsimmons at pcc.edu> 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.
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 :-)
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