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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 M th 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 (Chernoff, 1954) and path independence (Arrow, 1963). We also examine the relationships between the outcomes of the two procedures. Then, we investigate under what conditions the outcomes of each procedure are independent of the order of lexicographic application of the criteria. Examples for applications of the results in the economic environments are also presented.

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Bibliographic Info

Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2007-13.

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Length: 23 p.
Date of creation: Nov 2007
Date of revision:
Handle: RePEc:hit:econdp:2007-13

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Related research

Keywords: multiple criteria for choice; lexicographic application; choice consistency; path independence; order independence;

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References

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  1. Houy Nicolas, 2007. "Rationality and Order-Dependent Sequential Rationality," Theory and Decision, Springer, vol. 62(2), pages 119-134, March.
  2. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
  3. Tadenuma, Koichi, 2002. "Egalitarian-Equivalence and the Pareto Principle for Social Preferences," Discussion Papers 2002-08, Graduate School of Economics, Hitotsubashi University.
  4. 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.
  5. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  6. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
  8. Suzumura, Kotaro, 1981. "On pareto-efficiency and the no-envy concept of equity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 367-379, December.
  9. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
  10. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
  11. 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.
  12. 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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Cited by:
  1. Sandroni, Alvaro & Cherepavov, Vadim & Feddersen, Timothy, 2013. "Rationalization," Theoretical Economics, Econometric Society, vol. 8(3), September.
  2. 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.
  3. 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).
  4. 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.
  5. Matsuki, Jun & Tadenuma, Koichi, 2013. "Choice via Grouping Procedures," Discussion Papers 2013-08, Graduate School of Economics, Hitotsubashi University.
  6. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Ozbay, 2009. "Revealed Attention," NajEcon Working Paper Reviews 814577000000000409, www.najecon.org.

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