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Revealed Preference Dimension via Matrix Sign Rank

  • Shant Boodaghians
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11316)

Abstract

Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the market dimension is fixed. This paper solves the open problem of determining exactly which graphs are attainable as revealed preference graphs in d-dimensional markets. This is achieved via an exact characterization which closely ties the feasibility of the graph to the Matrix Sign Rank of its signed adjacency matrix. The paper also shows that when the preference relations form a partially ordered set with order-dimension k, the graph is attainable as a revealed preference graph in a k-dimensional market.

Keywords

Revealed preference Matrix sign rank Partial order 

Notes

Acknowledgements

I would like to thank Ruta Mehta, Adrian Vetta, and Siddharth Barman, for their insightful discussion in the initial stages of work.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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