[EM] Alex Small FBC paper

[Warren Smith]

>The idea of the linearity condition is simply that the statements being checked are all linear inequalities.  In the very simplest case of plurality voting, candidate A would win if:
f(votes for A) - f(votes for B) > 0
AND
f(votes for A) - f(votes for C) > 0
AND
etc. for all other candidates

--a good name for that would be "polyhedral" voting methods.
I don't know why, since it seems to be an excellent concept -- and
you've shown it is useful -- but nobody (?) seems to have
discussed/named it before.

I was certainly aware (and probably many others too) that practically
everything was a polyhedral method, but few or no people ever actually
found a use for that observation before.

Well... actually I can think of some uses, but they were of a
quite different character.  Numerous authors have used it to assess
probabilities of phenomena via polyhedral-volume computations, and
I've used it to find the "best/simplest" election examples of
phenomena by solving a linear program to find the example.  You're
using it to make logical deductions to prove theorems.

>As for "*" vs. "x" for multiplication

--well, jeez, just use no symbol at all, AB = A*B, just like everybody else.
But if you insist on a symbol use cdot.  (I do use * when forced to write in
un-typeset ASCII.  But if you have a math typesetting program, why?)

>style...

--well, you're calling it style, but I think there is more to it than
that.  There's good reasons for what you call style.  What *I* would
label with the word style, is stuff for which there is NOT really good
reasons, and it really is more of a matter of personal choice.  Like
use of the first person singular.

E.g. theorem statements ought to be self-contained standalone
readable.  Definitions ought to be precise. This is not a mere matter
of style in my view.  If they aren't then you're abusing the words;
they aren't real, it is just a sham.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html