  A balanced pair in an ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements
of $V$ such that the proportion of linear extensions of $P$ that put $x$ before
$y$ is in the real interval $[1/3, 2/3]$. We define the notion of a good pair
and claim any ordered set that has a good pair will satisfy the conjecture and
furthermore every ordered set which is not totally ordered and has a forest as
its cover graph has a good pair.
