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Budget-balance, fairness and minimal manipulability

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  • Ehlers, Lars

    ()
    (Departement de Sciences Economiques and CIREQ, Universite de Montreal)

  • Svensson, Lars-Gunnar

    ()
    (Department of Economics, Lund University)

  • Andersson, Tommy

    ()
    (Department of Economics, Lund University)

Abstract

A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents. Fairness requires that each agent weakly prefers his consumption bundle to any other agent's bundle. In this context, fairness is incompatible with budget-balance and non-manipulability (Green and Laffont, 1979). Our approach here is to weaken or abandon non-manipulability. We search for the rules which are minimally manipulable among all fair and budget-balanced rules. First, we show for a given preference profile, all fair and budget-balanced rules are either (all) manipulable or (all) non-manipulable. Hence, measures based on counting profiles where a rule is manipulable or considering a possible inclusion of profiles where rules are manipulable do not distinguish fair and budget-balanced rules. Thus, a ``finer'' measure is needed. Our new concept compares two rules with respect to their degree of manipulability by counting for each profile the number of agents who can manipulate the rule. Second, we show that maximally preferred fair allocation rules are the minimally (individually and coalitionally) manipulable fair and budget-balanced allocation rules according to our new concept. Such rules choose allocations with the maximal number of agents for whom the utility is maximized among all fair and budget-balanced allocations.

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Article provided by Econometric Society in its journal Theoretical Economics.

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Handle: RePEc:the:publsh:1346

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Keywords: Minimal manipulability; fairness; budget-balance; allocation rules;

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References

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  1. Ning Sun & Zaifu Yang, 2003. "A General Strategy Proof Fair Allocation Mechanism," Working Papers 346, Bielefeld University, Center for Mathematical Economics.
  2. Atila Abdulkadiroglu & Tayfun Sonmez & M. Utku Unver, 2002. "Room assignment-rent division: A market approach," Discussion Papers, Columbia University, Department of Economics 0102-11, Columbia University, Department of Economics.
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  4. Andersson, T. & Svensson, L.-G. & Yang, Z., 2010. "Constrainedly fair job assignments under minimum wages," Games and Economic Behavior, Elsevier, vol. 68(2), pages 428-442, March.
  5. Andersson, Tommy & Svensson, Lars-Gunnar, 2008. "Non-manipulable assignment of individuals to positions revisited," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 350-354, November.
  6. Svensson, Lars-Gunnar, 2006. "Coalition Strategy-Proofness and Fairness," Working Papers 2006:10, Lund University, Department of Economics.
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  8. Andersson, Tommy & Svensson, Lars-Gunnar & Ehlers, Lars, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Working Papers 2010:16, Lund University, Department of Economics, revised 15 Jan 2013.
  9. Sun, Ning & Yang, Zaifu, 2003. "A general strategy proof fair allocation mechanism," Economics Letters, Elsevier, vol. 81(1), pages 73-79, October.
  10. Maus,Stefan & Peters,Hans & Storcken,Ton, 2005. "Anonymous voting and minimal manipulability," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  11. Claus-Jochen Haake & Matthias G. Raith & Francis Edward Su, 2002. "Bidding for envy-freeness: A procedural approach to n-player fair-division problems," Social Choice and Welfare, Springer, vol. 19(4), pages 723-749.
  12. Debasis Mishra & Dolf Talman, 2008. "Characterization of the walrasian equilibria of the assignment model," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 08-07, Indian Statistical Institute, New Delhi, India.
  13. Svensson, Lars-Gunnar, 1991. "Nash Implementation of Competitive Equilibria in a Model with Indivisible Goods," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 869-77, May.
  14. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  15. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer, vol. 17(2), pages 201-215.
  16. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 1023-39, July.
  17. Helmuts Azacis, 2004. "Double Implementation in a Market for Indivisible Goods with a Price Constraint," UFAE and IAE Working Papers 623.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  18. Stefan Maus & Hans Peters & Ton Storcken, 2007. "Minimal manipulability: anonymity and unanimity," Social Choice and Welfare, Springer, vol. 29(2), pages 247-269, September.
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  21. Parag A. Pathak & Tayfun Sönmez, 2011. "School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation," Boston College Working Papers in Economics 784, Boston College Department of Economics.
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Cited by:
  1. Ehlers, Lars & Svensson, Lars-Gunnar & Andersson, Tommy, 0. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, Econometric Society.
  2. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2012. "Least Manipulable Envy-free Rules in Economies with Indivisibilities," Working Papers 2012:8, Lund University, Department of Economics, revised 30 Sep 2013.
  3. Parag A. Pathak & Tayfun Sönmez, 2011. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," NBER Working Papers 16783, National Bureau of Economic Research, Inc.
  4. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Tommy Andersson & Lars Ehlers & Lars-Gunnar Svensson, 2012. "(Minimally) ?-Incentive Compatible Competitive Equilibria in Economies with Indivisibilities," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 04-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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