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Integer Programming and Arrovian Social Welfare Functions

Author

Listed:
  • Jay Sethuraman

    () (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Teo Chung Piaw

    () (Department of Decision Sciences, National University of Singapore, Singapore 119260)

  • Rakesh V. Vohra

    () (Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

Abstract

We characterize the class of Arrovian Social Welfare Functions (ASWFs) as integer solutions to a collection of linear inequalities. Many of the classical possibility, impossibility, and characterization results can be derived in a simple and unified way from this integer program. Among the new results we derive is a characterization of preference domains that admit a nondictatorial, neutral ASWF. We also give a polyhedral characterization of all ASWFs on single-peaked domains.

Suggested Citation

  • Jay Sethuraman & Teo Chung Piaw & Rakesh V. Vohra, 2003. "Integer Programming and Arrovian Social Welfare Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 309-326, May.
  • Handle: RePEc:inm:ormoor:v:28:y:2003:i:2:p:309-326
    DOI: 10.1287/moor.28.2.309.14478
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    File URL: http://dx.doi.org/10.1287/moor.28.2.309.14478
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    References listed on IDEAS

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    1. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    2. Chung-Piaw Teo & Jay Sethuraman, 1998. "The Geometry of Fractional Stable Matchings and Its Applications," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 874-891, November.
    3. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-1037, July.
    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    7. Muller, Eitan, 1982. "Graphs and Anonymous Social Welfare Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 609-622, October.
    8. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
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    Citations

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    Cited by:

    1. Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2014. "Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach," SIRE Discussion Papers 2015-21, Scottish Institute for Research in Economics (SIRE).
    2. Francesca Busetto & Giulio Codognato & Simone Tonin, 2017. "Nondictatorial Arrovian Social Welfare Functions, Simple Majority Rule and Integer Programming," Working Papers 2017_11, Durham University Business School.
    3. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    4. Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2014. "Integer Programming on Domains Containing Inseparable Ordered Paris," SIRE Discussion Papers 2015-22, Scottish Institute for Research in Economics (SIRE).
    5. repec:spr:reecde:v:22:y:2018:i:3:d:10.1007_s10058-018-0214-3 is not listed on IDEAS
    6. repec:eee:reecon:v:72:y:2018:i:4:p:428-434 is not listed on IDEAS

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