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Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?

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  • Salvador Barberà
  • Dolors Berga
  • Bernardo Moreno

Abstract

A social choice function may or may not satisfy a desirable property depending on its domain of definition. For the same reason, different conditions may be equivalent for functions defined on some domains, while different in other cases. Understanding the role of domains is therefore a crucial issue in mechanism design. We illustrate this point by analyzing the role of different conditions that are always related, but not always equivalent to strategy-proofness. We define two very natural conditions that are necessary for strategy-proofness: monotonicity and reshuffling invariance. We remark that they are not always sufficient. Then, we identify a domain condition, called intertwinedness, that ensures the equivalence between our two conditions and that of strategy-proofness. We prove that some important domains are intertwined: those of single-peaked preferences, both with public and private goods, and also those arising in simple models of house allocation. We prove that other necessary conditions for strategy-proofness also become equivalent to ours when applied to functions defined on intertwined domains, even if they are not equivalent in general. We also study the relationship between our domain restrictions and others that appear in the literature, proving that we are indeed introducing a novel proposal.

Suggested Citation

  • Salvador Barberà & Dolors Berga & Bernardo Moreno, 2011. "Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?," Working Papers 598, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:598
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    References listed on IDEAS

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    Cited by:

    1. Nozomu Muto & Shin Sato, 2016. "A decomposition of strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 277-294, August.
    2. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    3. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    4. Keisuke Bando & Kenzo Imamura, 2016. "A necessary and sufficient condition for weak Maskin monotonicity in an allocation problem with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 589-606, October.

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    More about this item

    Keywords

    strategy-proofness; reshuffling invariance; monotonicity; intertwined domains;
    All these keywords.

    JEL classification:

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

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