Attempt at logical english definition for CSSD (using beatpath winner).

[Clinton <cryptor@zip.com.au>]

Heres an attempt to describe the winner of a CSSD election logically, 
using the beatpath winner implimentation. I've tryed to structure it so 
that removing the parenthesis gives a plain english definition. Any 
comments would be appresiated.

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In the following definition all occurances of A and B refer to options.

(A is prefered over B on vote X) if
   (A is ranked higher than B on vote X) OR
   ((A is ranked on vote X) AND (B is not ranked on vote X))

(A beats B by X) if
   (X > 0) where
   X = number of unique votes Y such that (A is prefered over B on vote 
Y) -
       number of unique votes Z such that (B is prefered over A on vote Z)

(A has a beatpath to B by X) if
   (A beats B by X)

(A has a beatpath to B by X) if
   (A beats C by Y) AND (C has a beatpath to B by Z) where
   X = minimum of Y and Z

(A has a strongest beatpath to B by X) where
   Z is the set of unique elements Y such that (A has a beatpath to B by Y)
   X = largest element of Z, 0 if Z is empty.  

(A has a beatpath win to B) if
   (A has a strongest beatpath to B by Y) AND
   (B has a strongest beatpath to A by Z) AND
   (Y > Z)

(A is tied winner) if
   there is no B such that (B has a beatpath win to A)

(A is a winner) if
   there is no B such that (B is prefered over A on the casting vote)

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Clinton