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Note on the goodness-of-fit measure for GARP; NP-hardness of minimum cost index

Author

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  • Kohei Shiozawa

    (Graduate School of Economics, Osaka University)

Abstract

The purpose of this paper is to show that the problem of computing minimum cost index (MCI), which is proposed by Dean and Martin (2010, 2015) as a goodness-of-fit measure of GARP, is NP- hard. We show the result by using a reduction from maximum acyclic subgraph problem (MASP) which is a traditional decision problem known to be NP-complete.

Suggested Citation

  • Kohei Shiozawa, 2015. "Note on the goodness-of-fit measure for GARP; NP-hardness of minimum cost index," Discussion Papers in Economics and Business 15-18, Osaka University, Graduate School of Economics.
    • Handle: RePEc:osk:wpaper:1518
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    File URL: http://www2.econ.osaka-u.ac.jp/library/global/dp/1518.pdf
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    References listed on IDEAS

    as
    1. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    2. Mark Dean & Daniel Martin, 2016. "Measuring Rationality with the Minimum Cost of Revealed Preference Violations," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 524-534, July.
    3. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
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    Cited by:

    1. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev., Osaka University, Graduate School of Economics, revised Jul 2015.
    2. Victor H. Aguiar & Roberto Serrano, 2018. "Classifying bounded rationality in limited data sets: a Slutsky matrix approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 9(4), pages 389-421, November.

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    More about this item

    Keywords

    Revealed Preference; GARP; Goodness of Fit Measure; Minimum Cost Index; Com-putational Complexity;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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