Probabilistic Rationing with Categorized Priorities: Processing Reserves Fairly and Efficiently

In recent years, a market design approach for rationing problems with multi-category priorities has been considered for various applications including healthcare, immigration, and school choice. We consider a probabilistic or fractional approach to rationing that is geared towards achieving symmetry axioms such as anonymity and neutrality in conjunction to primary axioms such as eligibility compatibility, respect of priorities, and non-wastefulness. We present new algorithms for the problem that have advantages over the simultaneous reservation rule of Delacrétaz (ACM EC 2021) with respect to fairness, efficiency, and simplicity.