How to describe objects?

• Main Author: LIU PENG
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: Random assignment; sd-strategy-proofness; sd-efficiency; equal treatment of equals; lexicographically separable preferences; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1924; https://ink.library.smu.edu.sg/context/soe_research/article/2923/viewcontent/How_to_describe_houses.pdf
• Institution: Singapore Management University

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.