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The Computational Complexity of Rationalizing Behavior

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Listed author(s):
  • 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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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

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  1. Ariel Rubinstein, 2000. "Economics and Language," Online economics textbooks, SUNY-Oswego, Department of Economics, number lang1.
  2. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," NajEcon Working Paper Reviews 666156000000000082, www.najecon.org.
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  4. Apesteguia, Jose & Ballester, Miguel A., 2013. "Choice by sequential procedures," Games and Economic Behavior, Elsevier, vol. 77(1), pages 90-99.
  5. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
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  8. Johnson Mark R., 1995. "Ideal Structures of Path Independent Choice Functions," Journal of Economic Theory, Elsevier, vol. 65(2), pages 468-504, April.
  9. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
  10. Mandler, Michael & Manzini, Paola & Mariotti, Marco, 2012. "A million answers to twenty questions: Choosing by checklist," Journal of Economic Theory, Elsevier, vol. 147(1), pages 71-92.
  11. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," Discussion Paper Series dp320, The Federmann Center for the Study of Rationality, the 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. 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.
  14. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
  15. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
  16. Futia, Carl, 1977. "The complexity of economic decision rules," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 289-299, December.
  17. Amos Tversky & Itamar Simonson, 1993. "Context-Dependent Preferences," Management Science, INFORMS, vol. 39(10), pages 1179-1189, October.
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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. 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.
  3. Mandler, Michael, 2015. "Rational agents are the quickest," Journal of Economic Theory, Elsevier, vol. 155(C), pages 206-233.
  4. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
  5. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
  6. Salvador Barberà & Alejandro Neme, 2015. "Ordinal Relative Satisficing Behavior: Theory and Experiments," Working Papers 790, Barcelona Graduate School of Economics.
  7. COSAERT Sam, 2017. "What types are there?," LISER Working Paper Series 2017-01, LISER.
  8. 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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