We study the random assignment of indivisible objects among a set of agents with strict preferences. We show that there exists no mechanism which is unanimous, strategy-proof and envy-free. Weakening the first requirement to q-unanimity - i.e., when every agent ranks a different object at the...

In school choice problems, the widely used manipulable Immediate Acceptance mechanism (IA) disadvantages unsophisticated applicants, but may ex-ante Pareto dominate any strategy-proof alternative. In these cases, it may be preferable to aid applicants within IA, rather than to abandon it. In a...

The use of lotteries is advocated to desegregate schools. We study lottery quotas embedded in the two most common school choice mechanisms, namely deferred and immediate acceptance mechanisms. Some seats are allocated based on merit (e.g., grades) and some based on lottery draws. We focus on the...