Overview

A deterministic assignment that allocates a set of objects to some agents is popular if it is not popular-dominated, i.e., there is no other one where a majority of agents are better off. As the notion of popularity, i.e., democratic efficiency, is a refinement of Pareto efficiency, we introduce a weakly popular assignment as a Pareto assignment that is not popular-dominated by any popular assignment. We call a random assignment ex-post weakly popular if it has a lottery over weakly popular assignments. We introduce an upper-contour strategy proof rule that provides an ex-post weakly popular random assignment and satisfies equal treatment of equals and non-bossiness. Finally, we prove two strong impossibility results between ex-post popularity and fairness, in the sense of weak envy-freeness and equal division lower bound.