  We evaluate the goal of maximizing the number of individuals matched to
acceptable outcomes. We show that it implies incentive, fairness, and
implementation impossibilities. Despite that, we present two classes of
mechanisms that maximize assignments. The first are Pareto efficient, and
undominated -- in terms of number of assignments -- in equilibrium. The second
are fair for unassigned students and assign weakly more students than stable
mechanisms in equilibrium.
