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Notions of anonymity for object assignment: impossibility theorems

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  • Hikaru Kondo

    (Osaka University)

Abstract

We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents’ names are permuted, their assignments be permuted in the same way. Since no rule satisfies this definition, we introduce weaker variants, “anonymity for distinct preferences,” “pairwise-anonymity for distinct preferences,” “pairwise-anonymity for fully differentiated profiles,” and “independence of others’ permutations.” We show that for more than two agents and two objects, no rule is pairwise-anonymous for distinct preferences and Pareto-efficient (Theorem 1), no rule is pairwise-anonymous for distinct preferences and independent of others’ permutations (Theorem 2), and no rule is pairwise-anonymous for fully differentiated profiles and strategy-proof (Theorem 3).

Suggested Citation

  • Hikaru Kondo, 2019. "Notions of anonymity for object assignment: impossibility theorems," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 113-126, December.
    • Handle: RePEc:spr:reecde:v:23:y:2019:i:3:d:10.1007_s10058-019-00223-1
    DOI: 10.1007/s10058-019-00223-1
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    References listed on IDEAS

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    More about this item

    Keywords

    Impartiality; Anonymity; Indivisible goods;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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