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Fleurbaey–Michel conjecture on equitable weak Paretian social welfare order

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  • Dubey, Ram Sewak

Abstract

The paper examines the problem of explicit description of a social welfare order over infinite utility streams, which respects anonymity and weak Pareto axioms. It provides a complete characterization of the domains of one period utilities, for which it is possible to explicitly describe a weak Paretian social welfare order satisfying the anonymity axiom. For domains containing any set of order type similar to the set of positive and negative integers, every equitable social welfare order satisfying the weak Pareto axiom is non-constructive. The paper resolves a conjecture by Fleurbaey and Michel (2003) that there exists no explicit (that is, avoiding the axiom of choice or similar contrivances) description of an ordering which satisfies weak Pareto and indifference to finite permutations. It also provides an interesting connection between the existence of social welfare function and the constructive nature of social welfare order by showing that the domain restrictions for the two are identical.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 4-5 ()
Pages: 434-439

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Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:434-439

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Anonymity; Weak Pareto; Social welfare order; Non-Ramsey set; Order type;

References

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  1. Ram Sewak Dubey & Tapan Mitra, 2011. "On equitable social welfare functions satisfying the Weak Pareto Axiom: A complete characterization," International Journal of Economic Theory, The International Society for Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 231-250, 09.
  2. FLEURBAEY, Marc & MICHEL, Philippe, 1997. "Intertemporal equity and the extension of the Ramsey criterion," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1997004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Luc LAUWERS, 2009. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Center for Economic Studies - Discussion papers, Katholieke Universiteit Leuven, Centrum voor Economische Studiën ces09.05, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  4. Basu, Kaushik & Mitra, Tapan, 2003. "Aggregating Infinite Utility Streams with Inter-generational Equity: The Impossibility of Being Paretian," Working Papers 03-03, Cornell University, Center for Analytic Economics.
  5. Juan A. Crespo & Carmelo Núñez & Juan Pablo Rincón-Zapatero, 2007. "On the impossibility of representing infinite utility streams," Economics Working Papers we075530, Universidad Carlos III, Departamento de Economía.
  6. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1251-56, July.
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