Impossibilities for probabilistic assignment

Impossibilities for probabilistic assignment 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Social Choice and Welfare Springer Journals

Impossibilities for probabilistic assignment

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Public Finance; International Political Economy; Game Theory, Economics, Social and Behav. Sciences; Social Policy
ISSN
0176-1714
eISSN
1432-217X
D.O.I.
10.1007/s00355-017-1059-3
Publisher site
See Article on Publisher Site

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.

Journal

Social Choice and WelfareSpringer Journals

Published: May 29, 2017

References

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