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Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences

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  • Dolors Berga
  • Bernardo Moreno
  • Salvador BarberÃ

Abstract

We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules' range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones.

Suggested Citation

  • Dolors Berga & Bernardo Moreno & Salvador BarberÃ, 2015. "Domains, Ranges and Strategy-Proofness: The Case of Single-dipped Preferences," Working Papers 418, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:418
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    References listed on IDEAS

    as
    1. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
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    5. Vikram Manjunath, 2014. "Efficient and strategy-proof social choice when preferences are single-dipped," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 579-597, August.
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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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