It turns out my conjecture about undominated points is false! Here is the counterexample: N*(logN)^2 points sampled independently from a uniformly bounded probability density in the XY plane that is unimodal on lines, such that the expected number of undominated points is of order>=N: Consider the infinite width=1 rectangle bounded by the 3 lines X+Y=0, X+Y=1, and X=Y and containing (9, -8.5). The probability density is 0 outside the rectangle, and inside it is given by C/(z*ln(z)^2) where z=X-Y+9 and C>0 is an appropriate normalization constant. I do not know whether my conjecture about convex hull vertices is true, but I have a proof sketch that it is true, which perhaps can be turned into a proof... -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)