Decomposing random mechanisms

Marek Pycia and Utku Unver

Journal of Mathematical Economics, 2015, vol. 61, issue C, 21-33

Abstract: Random mechanisms have been used in real-life situations for reasons such as fairness. Voting and matching are two examples of such situations. We investigate whether the desirable properties of a random mechanism survive decomposition of the mechanism as a lottery over deterministic mechanisms that also hold such properties. To this end, we represent properties of mechanisms–such as ordinal strategy-proofness or individual rationality–using linear constraints. Using the theory of totally unimodular matrices from combinatorial integer programming, we show that total unimodularity is a sufficient condition for the decomposability of linear constraints on random mechanisms. As two illustrative examples we show that individual rationality is totally unimodular in general, and that strategy-proofness is totally unimodular in some individual choice models. We also introduce a second, more constructive approach to decomposition problems, and prove that feasibility, strategy-proofness, and unanimity, with and without anonymity, are decomposable in non-dictatorial single-peaked voting domains. Just importantly, we establish that strategy-proofness is not decomposable in some natural problems.

Keywords: Random mechanisms; Total unimodularity; Single-peaked preferences; Individual rationality; Strategy-proofness; Universal truthfulness (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (26)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304406815000579
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Decomposing Random Mechanisms (2014)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:61:y:2015:i:c:p:21-33

DOI: 10.1016/j.jmateco.2015.06.002

Access Statistics for this article

Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii

More articles in Journal of Mathematical Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().