A Fair and Optimal Approach to Sequential Healthcare Rationing

TL;DR

This paper tackles fair and efficient health-resource allocation under scarcity by modeling reserve systems with category-specific priorities and four fundamental axioms. It introduces two main mechanisms: Maximum Matching Adjustment (MMA) for the basic reserve model and Sequential Category Updating (SCU) for sequential/combined processing, each fulfilling eligibility compliance, non-wastefulness, respect for priorities, and maximum cardinality. MMA offers a simpler, faster alternative to prior methods like Reverse Rejecting, with a runtime of $O(|E|\sqrt{|V|})$ and a complete characterization of axiom-satisfying matchings; SCU extends to sequential settings and is unique under strict category precedence, with additional consistency and incentive guarantees. The paper also provides flow-network and bipartite-graph implementations of SCU, enabling scalable, practical deployment in real-world healthcare rationing (e.g., vaccine distribution and ICU-resource allocation) while preserving fairness and efficiency under heterogeneous priorities.

Abstract

The COVID-19 pandemic underscored the urgent need for fair and effective allocation of scarce resources, from hospital beds to vaccine distribution. In this paper, we study a healthcare rationing problem where identical units of a resource are divided into different categories, and agents are assigned based on priority rankings. % We first introduce a simple and efficient algorithm that satisfies four fundamental axioms critical to practical applications: eligible compliance, non-wastefulness, respect for priorities, and maximum cardinality. This new algorithm is not only conceptually simpler but also computationally faster than the Reverse Rejecting rules proposed in recent work. % We then extend our analysis to a more general sequential setting, where categories can be processed both sequentially and simultaneously. For this broader framework, we introduce a novel algorithm that preserves the four fundamental axioms while achieving additional desirable properties that existing rules fail to satisfy. Furthermore, we prove that when a strict precedence order over categories is imposed, this rule is the unique mechanism that satisfies these properties.

Figures (3)

• Figure 1: The eligibility graph for Example \ref{['example:instance']}, with the priority profile shown on the right.
• Figure 2: A network flow for Example \ref{['example:flow']}, where each edge is associated with a pair $(\ell, u)$, with $\ell$ denoting the lower bound and $u$ the upper bound. Pairs $(0, 1)$ are omitted for brevity.
• Figure 3: A compact network flow representation for Example \ref{['example:flow']}, where agents are partitioned into two groups based on their eligible categories. Specifically, group $k_1$ consists of agents $\{i_1, i_2, i_3\}$, while group $k_2$ consists of agents $\{i_4, i_5, i_6\}$. The lower and upper bounds are adjusted accordingly. Pairs $(0, 1)$ are omitted for brevity.

Theorems & Definitions (50)

• Example 1
• Definition 1: Eligibility Compliance
• Definition 2: Respect for Priorities
• Definition 3: Non-wastefulness
• Definition 4: Maximum Cardinality
• Definition 5: No Incentive to Hide
• Definition 6: Respect for Improvements
• Proposition 1
• proof
• Definition 7: Independence of Baseline Priority