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

`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)
---
Clinton

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