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On compromising freedom of choice and subjective

Nicolas Fayard, Marc Pirlot, Alexis Tsoukiàs

TL;DR

This paper extends the Capability Approach by proposing a compromise measure of freedom that jointly accounts for the diversity of options and their valuation. It defines a formal capability-set framework, contrasts instrumental and intrinsic extremes, and introduces an integral-based valuation $\Phi^{\phi}_v(\mathbf{A}) = \int_{\mathbf{A}^{\mathcal{D}}} \phi(v(\vec{a})) d\vec{a}$, where $\phi$ encodes different freedom interpretations. By bounding the measure between the intrinsic and instrumental extremes, and providing examples with $\phi(v)=v$, $\phi(v)=v^2$, and $\phi(v)=\sqrt{v}$, the approach offers a flexible, axiomatized way to capture individual preferences over diverse options. Computationally, it relies on Pareto-frontier representations and inclusion–exclusion, highlighting scalability challenges and suggesting directions for efficient approximation and empirical elicitation of $\phi$.

Abstract

This paper proposes a new framework for evaluating capability sets by incorporating individual preferences over the diversity of accessible options. Building on the Capability Approach, we introduce a compromise method that balances between the notions of negative and positive freedom, effectively capturing the intrinsic and instrumental values of diverse choices within capability sets.

On compromising freedom of choice and subjective

TL;DR

This paper extends the Capability Approach by proposing a compromise measure of freedom that jointly accounts for the diversity of options and their valuation. It defines a formal capability-set framework, contrasts instrumental and intrinsic extremes, and introduces an integral-based valuation , where encodes different freedom interpretations. By bounding the measure between the intrinsic and instrumental extremes, and providing examples with , , and , the approach offers a flexible, axiomatized way to capture individual preferences over diverse options. Computationally, it relies on Pareto-frontier representations and inclusion–exclusion, highlighting scalability challenges and suggesting directions for efficient approximation and empirical elicitation of .

Abstract

This paper proposes a new framework for evaluating capability sets by incorporating individual preferences over the diversity of accessible options. Building on the Capability Approach, we introduce a compromise method that balances between the notions of negative and positive freedom, effectively capturing the intrinsic and instrumental values of diverse choices within capability sets.

Paper Structure

This paper contains 20 sections, 5 theorems, 58 equations, 9 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. A formal framework for Capability sets
  3. Freedom of choice
  4. Gaertner and Xu method
  5. On ranking linear budget sets in terms of freedom of choice
  6. Extremes of freedom valuation and desirable properties
  7. Instrumental extreme
  8. Intrinsic extreme
  9. Desirable properties
  10. Compromise approach
  11. Definition
  12. Algorithms and complexity
  13. Conclusion
  14. Proof of Proposition \ref{['prop:ADPAcapaSets']}
  15. Proof of axioms for the compromise approach
  16. ...and 5 more sections

Key Result

Proposition 1

If $\mathbf{A} \subseteq \mathbb{R}^{h^*}_{\geq0}$ is compact, then for all $\vec{a} \in \mathbf{A}$, there exists $\vec{b} \in P(\mathbf{A})$ such that $\vec{b} \geq \vec{a}$.

Figures (9)

  • Figure 1: Three Capability sets and their PDC
  • Figure 6: An example of the determination of scores for some capability sets using Gaertner-Xu like method
  • Figure 7: An example of the determination of scores for some capability sets using optimistic and pessimistic Gaertner-Xu like methods
  • Figure 8: Two symmetric capability sets
  • Figure 9: Example \ref{['ex:max_ass']}: Instrumental extreme approach
  • ...and 4 more figures

Theorems & Definitions (12)

  • Definition 2.1
  • Example 1
  • Definition 2.2
  • Proposition 1
  • Corollary 1
  • Proposition 2
  • Example 2
  • Example 3
  • Example 4
  • Example 4: Cont.
  • ...and 2 more