Decomposing Random Mechanisms

39 Pages Posted: 14 Dec 2012 Last revised: 1 Mar 2014

Marek Pycia

University of California, Los Angeles (UCLA)

M. Utku Ünver

Boston College - Department of Economics

Date Written: February 1, 2014

Abstract

Ordinal random mechanisms have been used in real-life situations for reasons such as sustaining fairness or preventing collusion. Two examples of such domains are voting and matching. We investigate whether desirable properties of a random mechanism survive decomposition as a lottery over deterministic mechanisms that also hold such properties. To this end, we introduce a framework in which we can represent a random mechanism and its desirable properties such as strategy-proofness or individual rationality using linear constraints. Using the theory of totally unimodular incidence matrices from combinatorial integer programming, we introduce a sufficient condition for decomposability of linear constraints on random mechanisms. As two examples, we show that individual rationality is totally unimodular in general, and that strategy-proofness is totally unimodular in a certain individual choice model. However, strategy-proofness, unanimity, and feasibility together are not totally unimodular in collective choice environments in general. Thus, we introduce a direct constructive approach for such problems. Using this approach, we prove that feasibility, strategy-proofness, and unanimity, with and without anonymity, are decomposable on non-dictatorial single-peaked voting domains.

Keywords: random mechanisms, ordinal mechanisms, total unimodularity, single-peaked preferences, voting, individual rationality, strategy-proofness, unanimity, anonymity, generalized median mechanisms

JEL Classification: C60, D71, D72

Suggested Citation

Pycia, Marek and Ünver, M. Utku, Decomposing Random Mechanisms (February 1, 2014). Available at SSRN: https://ssrn.com/abstract=2189235 or http://dx.doi.org/10.2139/ssrn.2189235

Marek Pycia

University of California, Los Angeles (UCLA) ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095
United States

Utku Unver (Contact Author)

Boston College - Department of Economics ( email )

140 Commonwealth Ave.
Chestnut Hill, MA 02467
United States
+1 (617) 552 2217 (Phone)
+1 (617) 552 2318 (Fax)

HOME PAGE: http://www2.bc.edu/~unver

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