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Opportunity-Sensitive Social Welfare

T. Wienand, B. Magdalou, R. Nock, P. Hufe

Abstract

We develop an axiomatic framework to evaluate income distributions from the perspective of an opportunity-egalitarian social planner. Building on a formal link with the literature on decision theory under ambiguity, we characterize a class of opportunity-sensitive social welfare functions based on a two-stage evaluation: the planner first computes the expected utility of income within each social type, where types consist of individuals sharing the same circumstances beyond their control, and then aggregates these type-specific welfare levels through a transformation reflecting aversion to inequality of opportunity. The evaluation is governed by a single parameter. We provide equivalent representations of the social welfare function, including a mean-divergence form that separates an efficiency term from an inequality term, and we establish an opportunity stochastic dominance criterion. Finally, we derive inequality measures that decompose overall inequality into within-group risk and between-group inequality of opportunity, providing a tractable basis for normative welfare analysis.

Opportunity-Sensitive Social Welfare

Abstract

We develop an axiomatic framework to evaluate income distributions from the perspective of an opportunity-egalitarian social planner. Building on a formal link with the literature on decision theory under ambiguity, we characterize a class of opportunity-sensitive social welfare functions based on a two-stage evaluation: the planner first computes the expected utility of income within each social type, where types consist of individuals sharing the same circumstances beyond their control, and then aggregates these type-specific welfare levels through a transformation reflecting aversion to inequality of opportunity. The evaluation is governed by a single parameter. We provide equivalent representations of the social welfare function, including a mean-divergence form that separates an efficiency term from an inequality term, and we establish an opportunity stochastic dominance criterion. Finally, we derive inequality measures that decompose overall inequality into within-group risk and between-group inequality of opportunity, providing a tractable basis for normative welfare analysis.

Paper Structure

This paper contains 10 sections, 9 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Setup
  3. Social planner's preferences
  4. Representation with a uniform type distribution
  5. Representation on the extended domain
  6. Equivalent representations and stochastic dominance
  7. Properties and comparative inequality of opportunity aversion
  8. Inequality of opportunity indices
  9. Conclusion
  10. Proofs

Key Result

Theorem 1

Let $q(s) = 1/ |\mathcal{S}|$ for all $s \in \mathcal{S}$, and $|\mathcal{S}| \geq 3$.Theorem theo-general and all other theorems in this section also work for $|\mathcal{S}| = 2$ when invoking an additional axiom called the 'Thomsen condition' Wa88De60. The social planner's preferences relation $\m where $U(\pi_s) = \sum_{y \in \mathcal{Y}} \pi_s(y) u(y)$ is the expected utility of type $s$ with

Theorems & Definitions (15)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Definition 1
  • Theorem 5
  • Definition 2
  • Theorem 6
  • Definition 3
  • Theorem 7
  • ...and 5 more