[EM] More falsity: Concavity is what we want, better that than , a triangle
bmbuck at 14850.com
Fri Sep 28 00:15:47 PDT 2001
Buddha Buck <bmbuck at 14850.com> writes:
> 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.
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
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