Social Choice and Welfare

, Volume 11, Issue 3, pp 241–252

A characterization of strategy-proof social choice functions for economies with pure public goods

  • Salvador Barberà
  • Matthew Jackson
Article

Abstract

We characterize strategy-proof social choice functions when individuals have strictly quasi-concave, continuous and satiated utility functions on convex subsets of IRm, representing preferences for the provision of m pure public goods. When specialized to the case m=1, these assumptions amount to requiring that preferences are single peaked, and for such a domain there exists a wide class of strategy-proof social choice functions. These were studied by Moulin (1980) under strong additional assumptions. Our first results characterize the complete class, after an appropriate extension of the single-peakedness condition. The new characterization retains the flavour of Moulin's elegant representation theorem. For the general m-dimensional case, previous results have shown that there is no efficient, strategy-proof, nondictatorial social choice function, even within the domain restrictions under consideration (Border and Jordan 1983; Zhou 1991). In fact, Zhou's powerful result indicates that nondictatorial strategy-proof s.c.f.'s will have a range of dimension one. This allows us to conclude with a complete characterization of all strategy-proof s.c.f.'s on IRm, because restrictions of preferences from our admissible class to one dimensional subsets satisfy the slightly generalized notion of single-peakedness that is used in our characterization for the case m=1. We feel that a complete knowledge of the class of strategy-proof mechanisms, in this as well as in other contexts, is an important step in the analysis of the trade-offs between strategy-proofness and other performance criteria, like efficiency.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Salvador Barberà
    • 1
  • Matthew Jackson
    • 2
  1. 1.Department of EconomicsUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Kellogg Graduate School of ManagementNorthwestern UniversityUSA

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