Well, before Craig gets hyped up about the necessity of ignoring voters
who fail to vote in either "before" (V) or "after" (V') case, in order for
my definition of monotonicity to operate with meaning, I'll amend the
following-
> Let Pi(A,B:V) represent the truth of whether voter i prefers candidate A
> over B in voting schema V.
>
> Let W(V) represent the set of winners of voting schema V
>
> For all V, all V', W(V)<>W(V') implies-
>
> there exists i, A, B such that A is an element of W(V), A is not an
> element of W(V'), B is an element of W(V'), B is not an element of W(V),
> not Pi(B,A,V),not Pi(A,B,V')
to read-
-------------------------------------------------------------------------------
Let Pi(A,B:V) represent the truth of whether voter i prefers candidate A
over B in voting schema V.
Let W(V) represent the set of winners of voting schema V
For all V, all V', W(V)<>W(V') implies-
there exists i, A, B such that A is an element of W(V), A is not an
element of W(V'), B is an element of W(V'), B is not an element of
W(V), and-
(i) not Pi(B,A,V) and Pi(B,A,V')
or
(ii) Pi(A,B,V) and not Pi(A,B,V')
-------------------------------------------------------------------------------
There we go.
