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Abstract

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 10 (1997)
Issue (Month): 2 ()
Pages: 305-333

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Handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:305-333

Note: Received: August 29, 1995; revised version June 26, 1996
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• D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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1. Dagan, Nir, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Journal of Economic Theory, Elsevier, vol. 69(1), pages 255-261, April.
   
   • Nir Dagan, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Economic theory and game theory 003, Nir Dagan.
2. Bettina Klaus & Hans Peters & Ton Storcken, 1998. "Strategy-proof division with single-peaked preferences and individual endowments," Social Choice and Welfare, Springer, vol. 15(2), pages 297-311.
   
   • Klaus, Bettina & Peters, Hans & Storcken, Ton, 1998. "Strategy-proof division with single-peaked preferences and individual endowments," Open Access publications from Maastricht University urn:nbn:nl:ui:27-12226, Maastricht University.
3. Thomson, W., 1991. "Population-Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked," RCER Working Papers 302, University of Rochester - Center for Economic Research (RCER).
   
   • Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer, vol. 5(2), pages 229-46, March.
4. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
   
   • Salvador Barbera, 1995. "Strategy-Proof Allotment Rules," Discussion Papers 1142, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
5. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
6. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
7. Moreno, Bernardo, 2002. "Single-peaked preferences, endowments and population-monotonicity," Economics Letters, Elsevier, vol. 75(1), pages 87-95, March.
8. Schmeidler, David & Vind, Karl, 1972. "Fair Net Trades," Econometrica, Econometric Society, vol. 40(4), pages 637-42, July.
9. Postlewaite, Andrew, 1979. "Manipulation via Endowments," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 255-62, April.

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Cited by:

1. Murat Atlamaz & Bettina Klaus, 2003. "Manipulation via Endowments in Exchange Markets with Indivisible Goods," UFAE and IAE Working Papers 598.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
   
   • Murat Atlamaz & Bettina Klaus, 2007. "Manipulation via Endowments in Exchange Markets with Indivisible Goods," Social Choice and Welfare, Springer, vol. 28(1), pages 1-18, January.
   • Atlamaz, Murat & Klaus, Bettina, 2007. "Manipulation via endowments in exchange markets with indivisible goods," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20029, Maastricht University.
2. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer, vol. 14(1), pages 1-15, March.
3. Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers 2009.114, Fondazione Eni Enrico Mattei.
   
   • Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer, vol. 38(2), pages 187-210, February.
4. Erik Ansink & Carmen Marchiori, 2009. "Reallocating Water: An Application of Sequent," Working Papers 2009.126, Fondazione Eni Enrico Mattei.
5. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
6. Özgür Kıbrıs & Serkan Küçükşenel, 2009. "Uniform trade rules for uncleared markets," Social Choice and Welfare, Springer, vol. 32(1), pages 101-121, January.
7. Nir Dagan, 1995. "Consistent solutions in exchange economies: A characterization of the price mechanism," Economics Working Papers 141, Department of Economics and Business, Universitat Pompeu Fabra.
   
   • Nir Dagan, 1995. "Consistent Solutions in Exchange Economies: a Characterization of the Price Mechanism," Economic theory and game theory 011, Nir Dagan.
8. Rahmi Ilkilic & Cagatay Kayi, 2012. "Allocation rules on networks," DOCUMENTOS DE TRABAJO 009380, UNIVERSIDAD DEL ROSARIO.
   
   • Ilkilic, Rahmi & Kayi, Cagatay, 2012. "Allocation rules on networks," MPRA Paper 37305, University Library of Munich, Germany.
9. Moreno, Bernardo, 2002. "Single-peaked preferences, endowments and population-monotonicity," Economics Letters, Elsevier, vol. 75(1), pages 87-95, March.
10. Klaus, Bettina, 1997. "The characterization of the uniform reallocation rule without Pareto optimality," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20361, Maastricht University.
11. Kibris, Ozgur & Kucuksenel, Serkan, 2005. "Trade rules for uncleared markets," Working Papers 1232, California Institute of Technology, Division of the Humanities and Social Sciences.
    
    • Özgür Kýbrýs & Serkan Küçükþenel, 2005. "Trade rules for uncleared markets," Microeconomics 0508002, EconWPA.
12. Schummer, J. & Thomson, W., 1996. "Two Derivations of the Uniform Rule and an Application to Bankruptcy," RCER Working Papers 423, University of Rochester - Center for Economic Research (RCER).
    
    • Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.

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