Distributive Justice and Inequality Awareness in Random Assignment Problems

We introduce a formal notion to define distributive justice in the random assignment problem that considers an assignment just if it has the lowest inequality in the distribution of envy among agents. A random assignment has a lower inequality than another one if the former has a lower total number of instances of envy at any level. A random assignment satisfies ex-post lowest inequality if it has a lottery decomposition into deterministic assignments with the lowest inequality. We show that an ex-post lowest inequality is a refinement of rank efficiency, in the sense of Featherstone (2020). Moreover, we introduce a weakly strategyproof rule called the serial entitled mechanism, which provides a random assignment with ex-post lowest inequality and satisfies equal treatment of equals