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On the structure of division rules

Author

Listed:
  • Roy, Souvik
  • Sadhukhan, Soumyarup

Abstract

We consider the problem of dividing one unit of an infinitely divisible object among a finite number of agents. We provide a characterization of all single-peaked domains on which the uniform rule is the unique division rule satisfying efficiency, strategy-proofness, and equal treatment of equals (ETE). We also provide a class of division rules satisfying these properties on the remaining single-peaked domains. Next, we consider non single-peaked domains and provide a characterization of all such domains on which the uniform rule satisfies efficiency, strategy-proofness, and ETE. We also show that under some mild richness conditions the uniform rule is the unique rule satisfying the mentioned properties on these domains. Finally, we provide a class of division rules satisfying efficiency, strategy-proofness, and ETE on the remaining non single-peaked domains. We conclude the paper by providing a wide range of applications to justify the usefulness of our results.

Suggested Citation

  • Roy, Souvik & Sadhukhan, Soumyarup, 2020. "On the structure of division rules," MPRA Paper 104402, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:104402
    as

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    References listed on IDEAS

    as
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    3. 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.
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    6. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    7. Hans Peters & Gert-Jan Otten & Oscar Volij, 1996. "Two characterizations of the uniform rule for division problems with single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 291-306.
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    More about this item

    Keywords

    division problems; efficiency; strategy-proofness; equal treatment of equals; single-peaked preferences; non single-peaked preferences; the uniform rule;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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