The computational complexity of rationalizing Pareto optimal choice behavior
AbstractWe 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.
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Bibliographic InfoPaper provided by Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces11.13.
Date of creation: Jun 2011
Date of revision:
Other versions of this item:
- Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer, vol. 42(3), pages 529-549, March.
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-25 (All new papers)
- NEP-GTH-2011-06-25 (Game Theory)
- NEP-NET-2011-06-25 (Network Economics)
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