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Goodness of fit measures for revealed preference tests: Complexity results and algorithms

Author

Listed:
  • Bram De Rock
  • Bart Smeulders
  • Laurens Cherchye
  • Frits Spieksma

Abstract

We provide results on the computational complexity of goodness-of-fit measures (i.e. Afriat's efficiency index, Varian's efficiency vector-index, and the Houtman-Maks index) associated with several revealed preference axioms (i.e. WARP, SARP, GARP, and HARP). These results explain the computational difficulties that have been observed in literature when computing these indices. Our NP-hardness results are obtained by reductions from the independent set problem. We also show that this reduction can be used to prove that no approximation algorithm achieving a ratio of O(n1-δ), δ > 0 exists for Varian's index, nor for Houtman-Maks'index (unless P = NP). Finally, we give an exact polynomial-time algorithm for finding Afriat's efficiency index.

Suggested Citation

  • Bram De Rock & Bart Smeulders & Laurens Cherchye & Frits Spieksma, 2013. "Goodness of fit measures for revealed preference tests: Complexity results and algorithms," ULB Institutional Repository 2013/162939, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/162939
    Note: SCOPUS: ar.j
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    Citations

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    Cited by:

    1. Bart Smeulders & Laurens Cherchye & Bram De Rock & Frits C. R. Spieksma, 2013. "The Money Pump as a Measure of Revealed Preference Violations: A Comment," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1248-1258.
    2. Kohei Shiozawa, 2015. "Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index," Economics Bulletin, AccessEcon, vol. 35(4), pages 2455-2461.
    3. Bart Smeulders & Laurens Cherchye & Bram Rock & Frits C. R. Spieksma & Fabrice Talla Nobibon, 2015. "Transitive preferences in multi-member households," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 243-254, October.
    4. Smeulders, Bart & Cherchye, Laurens & De Rock, Bram & Spieksma, Frits C.R. & Talla Nobibon, Fabrice, 2015. "Complexity results for the weak axiom of revealed preference for collective consumption models," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 82-91.
    5. 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.
    6. Fabrice Talla Nobibon & Bart Smeulders & Frits C. R. Spieksma, 2015. "A Note on Testing Axioms of Revealed Preference," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1063-1070, September.

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