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Impossibilities for probabilistic assignment

Haris Aziz () and Yoichi Kasajima ()
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Haris Aziz: Data61, CSIRO and UNSW
Yoichi Kasajima: Waseda University

Social Choice and Welfare, 2017, vol. 49, issue 2, 255-275

Abstract: 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.

Date: 2017
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