Skip to main content
SpringerLink
Log in

A characterization of the uniform rule with several commodities and agents

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

We consider a problem of allocating infinitely divisible commodities among a group of agents. More specifically, there are several commodities to be allocated and agents have continuous, strictly convex, and separable preferences. We establish that a rule satisfies strategy-proofness, unanimity, weak symmetry, and nonbossiness if and only if it is the uniform rule. This result extends to the class of continuous, strictly convex, and multidimensional single-peaked preferences.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adachi T (2010) The uniform rule with several commodities: a generalization of Sprumont’s characterization. J Math Econ 46: 952–964

    Article  Google Scholar 

  • Amorós P (2002) Single-peaked preferences with several commodities. Soc Choice Welf 19: 57–67

    Article  Google Scholar 

  • Anno H, Sasaki H (2009) Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities. Working Paper, Waseda University

  • Barberà S, Jackson MO (1995) Strategy-proof exchange. Econometrica 51: 51–87

    Article  Google Scholar 

  • Barberà S, Gul F, Stacchetti E (1993) Generalized median voter schemes and committees. J Econ Theory 61: 262–289

    Article  Google Scholar 

  • Barberà S, Jackson MO, Neme A (1997) Strategy-proof allotment rules. Games Econ Behav 18: 1–21

    Article  Google Scholar 

  • Barberà S, Massó J, Serizawa S (1998) Strategy-proof voting on compact ranges. Games Econ Behav 25: 272–291

    Article  Google Scholar 

  • Barberà S, Berga D, Moreno B (2010) Individual versus group strategy-proofness: when do they coincide?. J Econ Theory 145: 1648–1674

    Article  Google Scholar 

  • Bénassy JP (1982) The economics of market disequilibrium. Academic Press, New York

    Google Scholar 

  • Bogomolnaia A, Deb R, Ehlers L (2005) Strategy-proof assignment on the full preference domain. J Econ Theory 123: 161–186

    Article  Google Scholar 

  • Border KC, Jordan JS (1983) Straightforward elections, unanimity and phantom voters. Rev Econ Stud 50: 153–170

    Article  Google Scholar 

  • Ching S (1994) An alternative characterization of the uniform rule. Soc Choice Welf 11: 131–136

    Article  Google Scholar 

  • Ching S, Serizawa S (1998) A maximal domain for the existence of strategy-proof rules. J Econ Theory 78: 157–166

    Article  Google Scholar 

  • Ehlers L, Klaus B (2003) Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems. Soc Choice Welf 21: 265–280

    Article  Google Scholar 

  • Fleurbaey M, Maniquet F (1997) Implementability and horizontal equity imply no-envy. Econometrica 65: 1215–1219

    Article  Google Scholar 

  • Foley D (1967) Resource allocation and the public sector. Yale Econ Essays 7: 45–98

    Google Scholar 

  • Hatfield JW (2009) Strategy-proof, efficient, and nonbossy quota allocations. Soc Choice Welf 33: 505–515

    Article  Google Scholar 

  • Le Breton M, Sen A (1999) Separable preferences, strategyproofness, and decomposability. Econometrica 67: 605–628

    Article  Google Scholar 

  • Le Breton M, Zaporozhets V (2009) On the equivalence of coalitional and individual strategy-proofness properties. Soc Choice Welf 33: 287–309

    Article  Google Scholar 

  • Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66: 23–38

    Article  Google Scholar 

  • Massó J, Neme A (2001) Maximal domain of preferences in the division problem. Games Econ Behav 37: 367–387

    Article  Google Scholar 

  • Massó J, Neme A (2007) Bribe-proof rules in the division problem. Games Econ Behav 61: 331–343

    Article  Google Scholar 

  • Miyagawa E (2001) House allocation with transfers. J Econ Theory 100: 329–355

    Article  Google Scholar 

  • Mizobuchi H, Serizawa S (2006) Maximal domain for strategy-proof rules in allotment economies. Soc Choice Welf 27: 195–210

    Article  Google Scholar 

  • Morimoto S, Serizawa S, Ching S (2010) A characterization of the uniform rule with several commodities and agents. Osaka University, ISER discussion paper no. 769

  • Moulin H (1980) On strategy-proofness and single-peakedness. Public Choice 35: 437–456

    Article  Google Scholar 

  • Otten G, Peters H, Volij O (1996) Two characterizations of the uniform rule for division problems with single-peaked preferences. Econ Theory 7: 291–306

    Google Scholar 

  • Pápai S (2000) Strategyproof assignment by hierarchical exchange. Econometrica 68: 1403–1433

    Article  Google Scholar 

  • Sasaki H (2003) Limitation of efficiency: strategy-proofness and single-peaked preferences with many commodities. Working paper, Rice University

  • Satterthwaite MA, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev of Econ Stud 48: 587–597

    Article  Google Scholar 

  • Schummer J (2000) Eliciting preferences to assign positions and compensation. Games Econ Behav 30: 293–318

    Article  Google Scholar 

  • Serizawa S (1996) Strategy-proof and individually rational social choice functions for public good economies. Econ Theory 7: 501–512

    Google Scholar 

  • Serizawa S (2002) Inefficiency of strategy-proof rules for pure exchange economies. J Econ Theory 106: 219–241

    Article  Google Scholar 

  • Serizawa S (2006) Pairwise strategy-proofness and self-enforcing manipulation. Soc Choice Welf 26: 305–331

    Article  Google Scholar 

  • Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59: 509–519

    Article  Google Scholar 

  • Svensson L-G, Larsson B (2002) Strategy-proof and nonbossy allocation of indivisible goods and money. Econ Theory 20: 483–502

    Article  Google Scholar 

  • Thomson W (1990) The consistency principle. In: Ichiishi T, Neyman A, Tauman Y (eds) Game theory and applications, proceedings of the 1987 international conference, Ohio State University, Columbus, Ohio. Academic Press, pp 187–215

  • Thomson W (1994a) Consistent solutions to the problem of fair division when preferences are single-peaked. J Econ Theory 63: 219–245

    Article  Google Scholar 

  • Thomson W (1994b) Resource-monotonic solutions to the problem of fair division when preferences are single-peaked. Soc Choice Welf 11: 205–223

    Google Scholar 

  • Thomson W (1995) Population-monotonic solutions to the problem of fair division when preferences are single-peaked. Econ Theory 5: 229–246

    Article  Google Scholar 

  • Thomson W (1997) The replacement principle in economies with single-peaked preferences. J Econ Theory 76: 145–168

    Article  Google Scholar 

  • Thomson W (2004) Consistency and its converse: an elementary introduction. University of Rochester, Mimeo

    Google Scholar 

  • Thomson W (2010) Implementation of solutions to the problem of fair division when preferences are single-peaked. Rev Econ Des 14: 1–15

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki, 567-0047, Japan

    Shuhei Morimoto & Shigehiro Serizawa

  2. School of Economics and Finance, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong

    Stephen Ching

Authors
  1. Shuhei Morimoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shigehiro Serizawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephen Ching
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuhei Morimoto.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morimoto, S., Serizawa, S. & Ching, S. A characterization of the uniform rule with several commodities and agents. Soc Choice Welf 40, 871–911 (2013). https://doi.org/10.1007/s00355-011-0648-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-011-0648-9

Keywords

Search

Navigation