We study employment by lotto (Aldershof et al., 1999), a procedurally fair matching algorithm for the so-called stable marriage problem. We complement Aldershof et al.'s (1999) analysis in two ways. First, we give an alternative and intuitive description of employment by lotto in terms of a probabilistic serial dictatorship on the set of stable matchings. Second, we show that Aldershof et al.'s (1999) conjectures are correct for small matching markets but not necessarily correct for large matching markets.