  An old problem in discrete geometry, originating with Kupitz, asks whether
there is a fixed natural number $k$ such that every finite set of points in the
plane has a line through at least two of its points where the number of points
on either side of this line differ by at most $k$. We give a negative answer to
a natural variant of this problem, showing that for every natural number $k$
there exists a finite set of points in the plane together with a pseudoline
arrangement such that each pseudoline contains at least two points and there is
a pseudoline through any pair of points where the number of points on either
side of each pseudoline differ by at least $k$.
