  We demonstrate an infinite family of pseudoline arrangements, in which an
arrangement of n pseudolines has no member incident to more than 4n/9 points of
intersection. This shows the "Strong Dirac" conjecture to be false for
pseudolines.
  We also raise a number of open problems relating to possible differences
between the structure of incidences between points and lines versus the
structure of incidences between points and pseudolines.
