Uncertainty, equality, fraternity

Rush T Stewart

doi:10.1007/s11229-021-03217-1

Abstract

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting?

Highlights

The veil of ignorance is an important theoretical construction for moral and political philosophy
For Rawls, just arrangements of social institutions and general principles that govern them are those that members of a society would choose under a hypothetical state of ignorance about the citizens’ individual social and economic standing, their abilities, etc. (1971)
How should we model ignorance in Lerner’s intended setting? Here, I consider Lerner’s theorem in the setting of imprecise probabilities (IP)

Summary

Introduction

The veil of ignorance is an important theoretical construction for moral and political philosophy. Given Lerner’s particular formulation of ignorance and assumptions about individual and social welfare, the equal distribution maximizes expected social welfare. In the IP setting, we find that, from the assumption of total ignorance, we do not automatically arrive at egalitarianism, partially vindicating those skeptical of Lerner’s “jump” from complete ignorance to equal probability It depends, in part, on the IP generalization of expected utility that we adopt. One way to think about assumption A.4 is that a social planner tasked with deciding the distribution of income uses the uniform probability distribution over the possible matchings of utility functions to individuals. Theorem 1 Given (A.1), (A.2), (A.3), and (A.4), expected social welfare is maximized by z, the equal distribution of income. With no probabilistic assessments of the states whatsoever, it is, at the very least, extremely difficult to evaluate such choices

Complete ignorance

Choice under IP

Discussion