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The Computational Complexity of Rationalizing Behavior

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  • Apesteguia, Jose
  • Ballester, Miguel A.

Abstract

We study the computational complexity of rationalizing choice behavior. We do so by analyzing two polar cases, and a number of intermediate ones. In our most structured case, that is where choice behavior is defined in universal choice domains and satisfies the "weak axiom of revealed preference," finding the complete preorder rationalizing choice behavior is a simple matter. In the polar case, where no restriction whatsoever is imposed, either on choice behavior or on choice domain, finding a collection of complete preorders that rationalizes behavior turns out to be intractable. We also show that the task of finding the rationalizing complete preorders is equivalent to a graph problem. This allows the search for existing algorithms in the graph theory literature, for the rationalization of choice.

Suggested Citation

  • Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:3:p:356-363
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    Cited by:

    1. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    2. Bhavook Bhardwaj & Siddharth Chatterjee, 2022. "Decisions over Sequences," Papers 2203.00070, arXiv.org, revised Sep 2022.
    3. Mandler, Michael, 2015. "Rational agents are the quickest," Journal of Economic Theory, Elsevier, vol. 155(C), pages 206-233.
    4. Fabrice Talla Nobibon & Laurens Cherchye & Yves Crama & Thomas Demuynck & Bram De Rock & Frits C. R. Spieksma, 2016. "Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms," Operations Research, INFORMS, vol. 64(6), pages 1197-1216, December.
    5. Yongjie Yang & Dinko Dimitrov, 2019. "The complexity of shelflisting," Theory and Decision, Springer, vol. 86(1), pages 123-141, February.
    6. Alcantud, José Carlos R. & Cantone, Domenico & Giarlotta, Alfio & Watson, Stephen, 2023. "Rationalization of indecisive choice behavior by pluralist ballots," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    7. Sam Cosaert, 2019. "What Types are There?," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 533-554, February.
    8. Salvador Barberà & Alejandro Neme, 2015. "Ordinal Relative Satisficing Behavior: Theory and Experiments," Working Papers 790, Barcelona School of Economics.
    9. Ronen Gradwohl & Eran Shmaya, 2013. "Tractable Falsifiability," Discussion Papers 1564, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Jos'e Carlos R. Alcantud & Domenico Cantone & Alfio Giarlotta & Stephen Watson, 2022. "Rationalization of indecisive choice behavior by majoritarian ballots," Papers 2210.16885, arXiv.org.
    11. 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.
    12. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    13. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
    14. Piermont, Evan, 2017. "Context dependent beliefs," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 63-73.

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