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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 3 (May)
Pages: 356-363

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Handle: RePEc:eee:mateco:v:46:y:2010:i:3:p:356-363

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Rationalization Computational complexity NP-complete Arbitrary choice domains;

References

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  1. Johnson, Mark R. & Dean, Richard A., 2001. "Locally complete path independent choice functions and their lattices," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 53-87, July.
  2. Jose Apesteguia & Miguel A. Ballester, 2012. "Choice by sequential procedures," Economics Working Papers 1309, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Rubinstein,Ariel, 2000. "Economics and Language," Cambridge Books, Cambridge University Press, number 9780521789905, October.
  4. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
  5. Futia, Carl, 1977. "The complexity of economic decision rules," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 289-299, December.
  6. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Fact-Free Learning," Cowles Foundation Discussion Papers 1491, Cowles Foundation for Research in Economics, Yale University.
    • Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2003. "Fact-Free Learning," PIER Working Paper Archive 05-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2004.
    • Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2003. "Fact-Free Learning," PIER Working Paper Archive 03-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. Mandler, Michael & Manzini, Paola & Mariotti, Marco, 2008. "A Million Answers to Twenty Questions: Choosing by Checklist," IZA Discussion Papers 3377, Institute for the Study of Labor (IZA).
  8. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Discussion Paper Series dp278, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  9. Amos Tversky & Itamar Simonson, 1993. "Context-Dependent Preferences," Management Science, INFORMS, vol. 39(10), pages 1179-1189, October.
  10. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," NajEcon Working Paper Reviews 666156000000000082, www.najecon.org.
  11. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," Discussion Paper Series dp320, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  12. Johnson, Mark R., 1990. "Information, associativity, and choice requirements," Journal of Economic Theory, Elsevier, vol. 52(2), pages 440-452, December.
  13. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
  14. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
  15. Campbell, Donald E, 1978. "Realization of Choice Functions," Econometrica, Econometric Society, vol. 46(1), pages 171-80, January.
  16. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
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Citations

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Cited by:
  1. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer, vol. 42(3), pages 529-549, March.
  2. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
  3. Ronen Gradwohl & Eran Shmaya, 2013. "Tractable Falsifiability," Discussion Papers 1564, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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