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The Computational Complexity of Rationalizing Behavior

  • Apesteguia, Jose
  • Ballester, Miguel A.

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

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  1. Michael Mandler & Paola Manzini & Marco Mariotti, 2008. "A Million Answers to Twenty Questions: Choosing by Checklist," Working Papers 622, Queen Mary University of London, School of Economics and Finance.
  2. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Discussion Paper Series dp278, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  3. Jose Apesteguia & Miguel�Angel Ballester, 2012. "Choice By Sequential Procedures," Working Papers 615, Barcelona Graduate School of Economics.
  4. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
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  7. Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," NajEcon Working Paper Reviews 666156000000000082, www.najecon.org.
  8. Ariel Rubinstein, 2000. "Economics and Language," Online economics textbooks, SUNY-Oswego, Department of Economics, number lang1.
  9. Futia, Carl, 1977. "The complexity of economic decision rules," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 289-299, December.
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  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., 1995. "Ideal Structures of Path Independent Choice Functions," Journal of Economic Theory, Elsevier, vol. 65(2), pages 468-504, April.
  13. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
  14. Campbell, Donald E, 1978. "Realization of Choice Functions," Econometrica, Econometric Society, vol. 46(1), pages 171-80, January.
  15. Amos Tversky & Itamar Simonson, 1993. "Context-Dependent Preferences," Management Science, INFORMS, vol. 39(10), pages 1179-1189, October.
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  17. 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.
  18. Johnson, Mark R., 1990. "Information, associativity, and choice requirements," Journal of Economic Theory, Elsevier, vol. 52(2), pages 440-452, December.
  19. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
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