Arrovian theorems for economic domains. The case where there are simultaneously private and public goods
type: Item
instance of: scholarly article
title: Arrovian theorems for economic domains. The case where there are simultaneously private and public goods
zbMATH Open document ID: 0696.90003
DOI: 10.1007/BF01832916
author: Georges Bordes
author: Michel Le Breton
published in: Social Choice and Welfare
publication date: 1990-01-01T00:00:00Z
review text: After Arrow's famous impossibility result the question arose whether his result also applies to economic domains, i.e. situations in which the set of social alternatives is a set of public goods or a set of collections of private goods, or a combination of both public and private goods. For public goods, \textit{E. Kalai} and \textit{E. Muller} [J. Econ. Theory 16, 457-469 (1977; Zbl 0407.90005)] showed that Arrow's theorem holds, for private goods where the individuals are assumed to be interested solely in their own commodity bundle, \textit{E. Kalai} and \textit{Z. Ritz} [ibid. 22, 23-36 (1980; Zbl 0429.90006)] and the authors [ibid. 47, No.2, 257- 281 (1989; Zbl 0677.90003)] among others, have proved that Arrow's result still holds. For the case of both public and private goods, the present paper provides an analogous answer. It is proved that for standard domains where there are infinitely many public and private goods and where the individuals have continuous, strictly increasing and convex complete preorderings, every weakly Paretian Arrow social welfare function is dictatorial. An Arrow function is one which by definition satisfies the condition of independence of irrelevant alternatives. The model which the authors are working with considers a set of social alternatives such that each alternative is composed of n private components, one for each person, and a public component. The proof is established for so-called ultrasaturating domains which are related both to saturating domains, a requirement used in the case of purely public goods, and to hypersaturating domains, used in the case of private alternatives only. It is shown that a standard domain is ultrasaturating. Finally, the authors show that a version of \textit{A. Mas-Colell} and \textit{H. Sonnenschein}'s theorem [Rev. Econ. Studies (1972)] also holds for standard domains in the case of public and private goods. For both results, the requirement of an ultrasaturating domain is a sufficient conditi…
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 4141756
zbMATH Keywords: existence of a dictator
zbMATH Keywords: public goods
zbMATH Keywords: private goods
zbMATH Keywords: Arrow social welfare function
zbMATH Keywords: Arrow function
zbMATH Keywords: ultrasaturating domains
zbMATH Keywords: hypersaturating domains
reviewed by: Wulf Gaertner
MaRDI profile type: Publication
cites work: Social welfare functions for economic environments with and without the Pareto principle
cites work: Arrovian theorems with private alternatives domains and selfish individuals
cites work: Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures
cites work: Characterization of the private alternatives domains admitting Arrow social welfare functions
cites work: Q3912303
cites work: General Possibility Theorems for Group Decisions
cites work: Restricted domains, Arrow social welfare functions and noncorruptible and nonmanipulable social choice correspondences: The case of private and public alternatives
cites work: Quasi-Transitivity, Rational Choice and Collective Decisions
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description: scientific article; zbMATH DE number 4141756