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.
| Original language | English |
|---|---|
| Pages (from-to) | 255-275 |
| Number of pages | 21 |
| Journal | Social Choice and Welfare |
| Volume | 49 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2017 Aug 1 |
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ASJC Scopus subject areas
- Social Sciences (miscellaneous)
- Economics and Econometrics
Cite this
Impossibilities for probabilistic assignment. / Aziz, Haris; Kasajima, Yoichi.
In: Social Choice and Welfare, Vol. 49, No. 2, 01.08.2017, p. 255-275.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Impossibilities for probabilistic assignment
AU - Aziz, Haris
AU - Kasajima, Yoichi
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.
UR - http://www.scopus.com/inward/record.url?scp=85019729785&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019729785&partnerID=8YFLogxK
U2 - 10.1007/s00355-017-1059-3
DO - 10.1007/s00355-017-1059-3
M3 - Article
AN - SCOPUS:85019729785
VL - 49
SP - 255
EP - 275
JO - Social Choice and Welfare
JF - Social Choice and Welfare
SN - 0176-1714
IS - 2
ER -