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Endogenous Inequality Aversion: Decision criteria for triage and other ethical tradeoffs

Federico Echenique, Teddy Mekonnen, M. Bumin Yenmez

TL;DR

This paper develops a formal theory of self-referential social welfare rules in which inequality aversion changes with the society’s aggregate welfare. It introduces Fan social welfare functions, where the relevant set of welfare weights $Pi(v)$ depends on the welfare level $v$, yielding fixed-point representations $u_{Pi}(x)$. The authors prove two main representation theorems corresponding to monotone increasing and monotone decreasing fans, linking triage-like decisions to crisis conditions and non-crisis states. The ventilator allocation application shows a threshold policy: as scarcity rises or vulnerability grows, the optimal rule shifts between Rawlsian (worst-off) and utilitarian (efficiency) criteria; the framework extends to educational spending and income distribution, illustrating broad utility for policy design under varying aggregate welfare. Together, the results formalize crisis-aware decision rules and offer a rigorous lens on welfare-driven policy pivots in crises such as pandemics and economic downturns, with a fixed-point mechanism that endogenizes inequality aversion.

Abstract

Medical ``Crisis Standards of Care'' call for a utilitarian allocation of scarce resources in emergencies, while favoring the worst-off under normal conditions. Inspired by such triage rules, we introduce social welfare functions whose distributive tradeoffs depend on the prevailing level of aggregate welfare. These functions are inherently self-referential: they take the welfare level as an input, even though that level is itself determined by the function. In our formulation, inequality aversion varies with welfare and is therefore self-referential. We provide an axiomatic foundation for a family of social welfare functions that move from Rawlsian to utilitarian criteria as overall welfare falls, thereby formalizing triage guidelines. We also derive the converse case, in which the social objective shifts from Rawlsianism toward utilitarianism as welfare increases.

Endogenous Inequality Aversion: Decision criteria for triage and other ethical tradeoffs

TL;DR

This paper develops a formal theory of self-referential social welfare rules in which inequality aversion changes with the society’s aggregate welfare. It introduces Fan social welfare functions, where the relevant set of welfare weights depends on the welfare level , yielding fixed-point representations . The authors prove two main representation theorems corresponding to monotone increasing and monotone decreasing fans, linking triage-like decisions to crisis conditions and non-crisis states. The ventilator allocation application shows a threshold policy: as scarcity rises or vulnerability grows, the optimal rule shifts between Rawlsian (worst-off) and utilitarian (efficiency) criteria; the framework extends to educational spending and income distribution, illustrating broad utility for policy design under varying aggregate welfare. Together, the results formalize crisis-aware decision rules and offer a rigorous lens on welfare-driven policy pivots in crises such as pandemics and economic downturns, with a fixed-point mechanism that endogenizes inequality aversion.

Abstract

Medical ``Crisis Standards of Care'' call for a utilitarian allocation of scarce resources in emergencies, while favoring the worst-off under normal conditions. Inspired by such triage rules, we introduce social welfare functions whose distributive tradeoffs depend on the prevailing level of aggregate welfare. These functions are inherently self-referential: they take the welfare level as an input, even though that level is itself determined by the function. In our formulation, inequality aversion varies with welfare and is therefore self-referential. We provide an axiomatic foundation for a family of social welfare functions that move from Rawlsian to utilitarian criteria as overall welfare falls, thereby formalizing triage guidelines. We also derive the converse case, in which the social objective shifts from Rawlsianism toward utilitarianism as welfare increases.
Paper Structure (26 sections, 9 theorems, 43 equations, 2 figures)

This paper contains 26 sections, 9 theorems, 43 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Motivation: Triage in ventilator allocation
  3. Model
  4. Preliminary definitions and notation.
  5. Axioms.
  6. The "fan" social welfare function.
  7. An example.
  8. Main Results
  9. Monotone increasing fan
  10. Monotone decreasing fan
  11. Application: Ventilator allocation problem
  12. Additional applications
  13. Educational spending.
  14. Income distribution.
  15. More on triage.
  16. ...and 11 more sections

Key Result

Theorem 1

A preference $\succeq$ satisfies monotonicity, strong continuity, convexity, mixing invariance, and downwards homotheticity if and only if there exists a continuous and monotone increasing fan $\Pi$ such that $\mathbf{x}\succeq \mathbf{y}$ if and only if $u_{\Pi}(\mathbf{x})\geq u_{\Pi}(\mathbf{y})$

Figures (2)

  • Figure 1: Optimal policy depending on fraction vulnerable (Type $L$) patients and ventilator supply. The blue line illustrates the threshold $\alpha^*(k)$
  • Figure 2: Three examples of "fan" social welfare orderings

Theorems & Definitions (9)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Lemma 3
  • Lemma 4
  • Lemma 5