Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

When is it (im)possible to respect all individuals' preferences under uncertainty?

Kensei Nakamura

Abstract

When aggregating Subjective Expected Utility preferences, the Pareto principle leads to an impossibility result unless the individuals have a common belief. This paper examines the source of this impossibility in more detail by considering the aggregation of a general class of incomplete preferences that can represent gradual ambiguity perceptions. Our result shows that the planner cannot avoid ignoring some individuals unless there is a probability distribution that all individuals agree is most plausible. This means that even if individuals have similar ambiguity perceptions, the impossibility persists as long as some individual's most plausible belief differs even slightly from that of others.

When is it (im)possible to respect all individuals' preferences under uncertainty?

Abstract

When aggregating Subjective Expected Utility preferences, the Pareto principle leads to an impossibility result unless the individuals have a common belief. This paper examines the source of this impossibility in more detail by considering the aggregation of a general class of incomplete preferences that can represent gradual ambiguity perceptions. Our result shows that the planner cannot avoid ignoring some individuals unless there is a probability distribution that all individuals agree is most plausible. This means that even if individuals have similar ambiguity perceptions, the impossibility persists as long as some individual's most plausible belief differs even slightly from that of others.

Paper Structure

This paper contains 7 sections, 6 theorems, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Setup
  3. Results
  4. Discussion
  5. Violation of Transitivity and Independence
  6. The Converse of Theorem \ref{['thm:main']}
  7. Concluding Remarks

Key Result

Theorem 1

Suppose that for each $i\in N\cup \{ 0 \}$, $\succsim_i$ is a variational Bewley preference $(u_i, c_i)$ and Preference Diversity holds. Then, Standard Pareto implies that there exists $(\alpha, \beta) \in \mathbb{R}^n_+ \times \mathbb{R}$ such that

Figures (1)

  • Figure 1: The set $A$ and a separating hyperplane

Theorems & Definitions (15)

  • Definition 1: Variational Bewley Representations
  • Remark 1: Properties of variational Bewley preferences
  • Remark 2: Unboundedness
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • proof : Proof of Theorem \ref{['thm:main']}.
  • Remark 3
  • Proposition 1
  • proof
  • ...and 5 more