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Lexicographic compositions of multiple criteria for decision making

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  • Houy, Nicolas
  • Tadenuma, Koichi

Abstract

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of the first binary relation, and then within that set, chooses the maximal elements of the second binary relation, and iterates the procedure until the Mth binary relation. We show several distinct sets of conditions for the choice functions representing these two procedures to satisfy non-emptiness and choice-consistency conditions such as contraction consistency and path independence. We also examine the relationships between the outcomes of the two procedures. Finally we investigate under what conditions the outcomes of each procedure are independent of the order of lexicographic application of the criteria.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 4 (July)
Pages: 1770-1782

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1770-1782

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Multiple criteria for choice Lexicographic application Choice consistency Path independence Order independence;

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  1. Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, vol. 13(3), pages 361-379, December.
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  7. Tadenuma, Koichi, 2002. "Egalitarian-Equivalence and the Pareto Principle for Social Preferences," Discussion Paper 128, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  8. Arrow, Kenneth J, 1977. "Extended Sympathy and the Possibility of Social Choice," American Economic Review, American Economic Association, vol. 67(1), pages 219-25, February.
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Cited by:
  1. Rohan Dutta & Sean Horan, 2013. "Inferring Rationales from Choice : Identification for Rational Shortlist Methods," Cahiers de recherche 09-2013, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  2. Ludovic Renou & Karl H. Schlag, 2009. "From Ordients to Optimization: Substitution Effects without Differentiability," Discussion Papers in Economics 09/6, Department of Economics, University of Leicester.
  3. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Ozbay, 2009. "Revealed Attention," NajEcon Working Paper Reviews 814577000000000409, www.najecon.org.
  4. 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).
  5. C. Binder, 2014. "Plural identities and preference formation," Social Choice and Welfare, Springer, vol. 42(4), pages 959-976, April.
  6. Matsuki, Jun & Tadenuma, Koichi, 2013. "Choice via Grouping Procedures," CCES Discussion Paper Series 52, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
  7. Sandroni, Alvaro & Cherepavov, Vadim & Feddersen, Timothy, 2013. "Rationalization," Theoretical Economics, Econometric Society, vol. 8(3), September.

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