[EM] More falsity: Concavity is what we want, better that than , a triangle

[Buddha Buck]

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