Fair and efficient assignments with fractional endowments

In designing school choice mechanisms, a common objective is to ensure that different sections of society have a chance of attending certain schools. For example that students from disadvantaged neighborhoods have a chance of attending elite schools. We propose fractional endowments as a way of ensuring this objective: explicitly endow agents with the desired chances.

The resulting model raises a series of challenges. What is the relevant notion of (constrained) fairness, or (justified) envy? The standard notion of justified envy has no obvious counterpart in the model with endowments. Is there a tension between fairness and efficiency? In our paper we tackle these challenges, providing new notions of fairness, and showing that these notions are largely compatible with efficiency.