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Impossibilities for probabilistic assignment

Author

Listed:
  • Haris Aziz

    (Data61, CSIRO and UNSW)

  • Yoichi Kasajima

    (Waseda University)

Abstract

We consider the problem of assigning objects probabilistically among a group of agents who may have multi-unit demands. Each agent has linear preferences over the (set of) objects. The most commonly used extension of preferences to compare probabilistic assignments is by means of stochastic dominance, which leads to corresponding notions of envy-freeness, efficiency, and strategy-proofness. We show that equal treatment of equals, efficiency, and strategy-proofness are incompatible. Moreover, anonymity, neutrality, efficiency, and weak strategy-proofness are incompatible. If we strengthen weak strategy-proofness to weak group strategy-proofness, then when agents have single-unit demands, anonymity, neutrality, efficiency, and weak group strategy-proofness become incompatible.

Suggested Citation

  • Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    • Handle: RePEc:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1059-3
    DOI: 10.1007/s00355-017-1059-3
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    Cited by:

    1. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    2. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    3. Zhang, Jun, 2019. "Efficient and fair assignment mechanisms are strongly group manipulable," Journal of Economic Theory, Elsevier, vol. 180(C), pages 167-177.
    4. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.

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