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Revealed Preference Dimension via Matrix Sign Rank

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Web and Internet Economics (WINE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11316))

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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.

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Notes

  1. 1.

    These two conditions imply that the relation must be acyclic.

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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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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Shant Boodaghians

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  1. Shant Boodaghians
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Correspondence to Shant Boodaghians .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    George Christodoulou

  2. Universität Augsburg, Augsburg, Germany

    Tobias Harks

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Boodaghians, S. (2018). Revealed Preference Dimension via Matrix Sign Rank. In: Christodoulou, G., Harks, T. (eds) Web and Internet Economics. WINE 2018. Lecture Notes in Computer Science(), vol 11316. Springer, Cham. https://doi.org/10.1007/978-3-030-04612-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-04612-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04611-8

  • Online ISBN: 978-3-030-04612-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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