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The computational complexity of rationalizing Pareto optimal choice behavior

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  • Thomas Demuynck

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Abstract

We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two. Copyright Springer-Verlag Berlin Heidelberg 2014

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 42 (2014)
Issue (Month): 3 (March)
Pages: 529-549

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Handle: RePEc:spr:sochwe:v:42:y:2014:i:3:p:529-549

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Related research

Keywords: Pareto efficiency; Computational complexity; NP-complete; C60; C63; D70;

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  1. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
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  13. Talla Nobibon, Fabrice & Spieksma, Frits C.R., 2010. "On the complexity of testing the Collective Axiom of Revealed Preference," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 123-136, September.
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Cited by:
  1. 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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