A framework for expected capability sets
Nicolas Fayard, David Ríos Insua, Alexis Tsoukiàs
TL;DR
The paper reframes decision-aiding under multiobjective uncertainty through Sen's capability approach, replacing a single utility with capability sets $U(f_m(s_l)) \subseteq \mathbb{R}^{h^*}_+$ and considering states $S$ with known probabilities $p(s_l)$. It introduces two mixing procedures: the natural but sometimes inadequate average capability set $\overline{\mathbf{A}}$, and the more principled expected capability set $E(\mathbf{A})$, defined via multiobjective optimization to preserve normative properties and Pareto dominance across states. The authors establish key properties for $E(\mathbf{A})$ (consistency with expected utility in simple cases, domination relations, linearity, and monotonicity) and compare $E(\mathbf{A})$ with $\overline{\mathbf{A}}$, showing $E(\mathbf{A})$ is typically more suitable for state-based policy design while $\overline{\mathbf{A}}$ suits social aggregation. They discuss computational challenges (MI-MOLP formulations, dependence on $l^*$ and $h^*$) and suggest contexts where each approach is preferable, along with directions for future work in broader decision settings and applications beyond welfare economics.
Abstract
This paper addresses decision-aiding problems that involve multiple objectives and uncertain states of the world. Inspired by the capability approach, we focus on cases where a policy maker chooses an act that, combined with a state of the world, leads to a set of choices for citizens. While no preferential information is available to construct importance parameters for the criteria, we can obtain likelihoods for the different states. To effectively support decision-aiding in this context, we propose two procedures that merge the potential set of choices for each state of the world taking into account their respective likelihoods. Our procedures satisfy several fundamental and desirable properties that characterize the outcomes.