Lexicographic Compositions of Multiple Criteria for Decision Making
AbstractThis 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 InfoPaper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2007-13.
Length: 23 p.
Date of creation: Nov 2007
Date of revision:
multiple criteria for choice; lexicographic application; choice consistency; path independence; order independence;
Other versions of this item:
- Houy, Nicolas & Tadenuma, Koichi, 2009. "Lexicographic compositions of multiple criteria for decision making," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1770-1782, July.
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances
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- Houy Nicolas, 2007. "Rationality and Order-Dependent Sequential Rationality," Theory and Decision, Springer, vol. 62(2), pages 119-134, March.
- Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
- Tadenuma, Koichi, 2002.
"Egalitarian-Equivalence and the Pareto Principle for Social Preferences,"
2002-08, Graduate School of Economics, Hitotsubashi University.
- Koichi Tadenuma, 2005. "Egalitarian-equivalence and the Pareto principle for social preferences," Social Choice and Welfare, Springer, vol. 24(3), pages 455-473, 06.
- 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.
- 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.
- 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.
- Elisha A. Pazner & David Schmeidler, 1975.
"Egalitarian Equivalent Allocations: A New Concept of Economic Equity,"
174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 671-87, November.
- Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
- 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.
- Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
- 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.
- Tadenuma, Koichi, 1998. "Efficiency First or Equity First?: Two Principles and Rationality of Social Choice," Discussion Papers 1998-01, Graduate School of Economics, Hitotsubashi University.
- 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.
- Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
- Sandroni, Alvaro & Cherepavov, Vadim & Feddersen, Timothy, 2013. "Rationalization," Theoretical Economics, Econometric Society, vol. 8(3), September.
- Rohan Dutta & Sean Horan, 2013. "Inferring Rationales from Choice : Identification for Rational Shortlist Methods," Cahiers de recherche 09-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- 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).
- Mandler, Michael & Manzini, Paola & Mariotti, Marco, 2012. "A million answers to twenty questions: Choosing by checklist," Journal of Economic Theory, Elsevier, vol. 147(1), pages 71-92.
- 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.
- 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.
- Matsuki, Jun & Tadenuma, Koichi, 2013.
"Choice via Grouping Procedures,"
2013-08, Graduate School of Economics, Hitotsubashi University.
- Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Ozbay, 2009.
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