This paper addresses the problem of randomly allocating n indivisible objects to n agents where each object can be evaluated according to a set of characteristics. The planner chooses a subset of characteristics and a ranking of them. Then she describes each object as a list of values according to the ranking of those chosen characteristics. Being informed of such a description, each agent figures out her preference that is lexicographically separable according to the characteristics chosen and ranked by the planner. Hence a description of the objects induces a collection of admissible preferences. We call a description good if it induces a preference domain that admits an sd-strategy-proof, sd-efficient, and equal-treatment-of-equals rule.When problem size n satisfies two technical assumptions, a description is good if and only if it is a binary tree, i.e., for each feasible combination of values of the top-t ranked characteristics, the following-up characteristic takes at most two feasible values.1 In addition, whenever the description is a binary tree, the probabilistic serial rule (Bogomolnaia and Moulin (2001)) satisfies all three axioms.
Random assignment, sd-strategy-proofness, sd-efficiency, equal treatment of equals, lexicographically separable preferences
How to describe objects?. (2017). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1924
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