The quadratic blocker conjecture for point sets in convex position

A finite point set is in convex position if every point is a vertex of its convex hull. A blocker for such a set is a point, outside the set, lying on an edge segment determined by two points of the set; the number of blockers is minimized over blocking sets. Convex-position blocker conjecture. Every set of $n$ points in convex position requires $\Omega(n^2)$ blockers. The source notes a lower bound of order $n\log n$ and a quadratic lower bound for equally spaced points on a circle, but the asserted quadratic order for arbitrary convex-position sets remains open.