Strategy-proof and envy-free random assignment

Arbeitspapier

We study the random assignment of indivisible objects among a set of agents with strict preferences. We show that there exists no mechanism which is unanimous, strategy-proof and envy-free. Weakening the first requirement to q-unanimity - i.e., when every agent ranks a different object at the top, then each agent shall receive his most-preferred object with probability of at least q - we show that a mechanism satisfying strategy-proofness, envy-freeness and ex-post weak non-wastefulness can be q-unanimous only for q È 2/n (where n is the number of agents). To demonstrate that this bound is tight, we introduce a new mechanism, Random-Dictatorship-cum-Equal-Division (RDcED), and show that it achieves this maximal bound when all objects are acceptable. In addition, for three agents, RDcED is characterized by the first three properties and ex-post weak efficiency. If objects may be unacceptable, strategy-proofness and envy-freeness are jointly incompatible even with ex-post weak non-wastefulness.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: WZB Discussion Paper ; No. SP II 2022-208

Classification and Topics

• Classification: Wirtschaft ; Equity, Justice, Inequality, and Other Normative Criteria and Measurement ; Analysis of Collective Decision-Making: General
• Subject: random assignment ; strategy-proofness ; envy-freeness ; q-unanimity

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Basteck, Christian ; Ehlers, Lars H.
• Event: Veröffentlichung
• (who): Wissenschaftszentrum Berlin für Sozialforschung (WZB)
• (where): Berlin
• (when): 2022

Further information

• Handle: http://hdl.handle.net/10419/268274
• Last update: 10.03.2025, 11:44 AM CET