TY - JOUR
T1 - Impossibilities for probabilistic assignment
AU - Aziz, Haris
AU - Kasajima, Yoichi
N1 - Funding Information:
Two independent papers, Aziz () and Kasajima (), were merged into the current paper. Kasajima () was based on a chapter of his Ph.D. thesis at the University of Rochester. Aziz is supported by a Julius Career Award. Kasajima acknowledges support from the JSPS KAKENHI Grant Numbers 22830102 and 16K03561.
Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00355-017-1059-3
DO - 10.1007/s00355-017-1059-3
M3 - Article
AN - SCOPUS:85019729785
SN - 0176-1714
VL - 49
SP - 255
EP - 275
JO - Social Choice and Welfare
JF - Social Choice and Welfare
IS - 2
ER -