Random Decision Making

In his Democratic Authority, David Estlund claims that "Democratic legitimacy requires that the procedure can be held, in terms acceptable to all qualified points of view, to be epistemically the best (or close to it) among those that are better than random" (p. 98). I've always been somewhat unsure what the 'better than random' bit is doing; if the best procedure is random, why isn't that enough? This Dilbert strip seems to make the point.