Revealed group preferences on non-convex choice problems
The authors investigate choice functions and choice correspondences where the collective choice problem is not necessarily convex. Let \(\Omega^n\) denote the class of compact, comprehensive subsets of \(R^n_+\) with non-empty interior. Then \(S \in \Omega^n\) may not be convex. The authors' first result is that there are no UpperHemiContinuous (UHC) choice functions (i.e., single-valued choice correspondences) on \(\Omega^n\) satisfying Strong Pareto Optimality (SPO). However, lifting the single-valuedness restriction, the authors obtain the following sharp characterization of choice correspondences: A UHC choice correspondence on \(\Omega^n\) satisfies SPO, Arrow's Choice Axiom, and a compromization condition if and only if it is regularly representable (Theorem 2). As an application, the authors characterize Choquet bargaining solutions.
scientific article; zbMATH DE number 1310143