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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
- Tadenuma, Koichi, 1998.
"Efficiency First or Equity First?: Two Principles and Rationality of Social Choice,"
1998-01, Graduate School of Economics, Hitotsubashi University.
- 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, 2002.
"Egalitarian-Equivalence and the Pareto Principle for Social Preferences,"
128, Center for Intergenerational Studies, Institute of Economic Research, 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 Papers 2002-08, Graduate School of Economics, 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.
- Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, 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.
- Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
- Houy Nicolas, 2007. "Rationality and Order-Dependent Sequential Rationality," Theory and Decision, Springer, vol. 62(2), pages 119-134, March.
- 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.
- Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
- 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.
- 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,"
CCES Discussion Paper Series
52, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
- Michael Mandler & Paola Manzini & Marco Mariotti, 2008.
"A Million Answers to Twenty Questions: Choosing by Checklist,"
622, Queen Mary, University of London, School of Economics and Finance.
- 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.
- 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).
- 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.
- Sandroni, Alvaro & Cherepavov, Vadim & Feddersen, Timothy, 2013. "Rationalization," Theoretical Economics, Econometric Society, vol. 8(3), September.
- Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Ozbay, 2009.
NajEcon Working Paper Reviews
- C. Binder, 2014. "Plural identities and preference formation," Social Choice and Welfare, Springer, vol. 42(4), pages 959-976, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Digital Resources Section, Hitotsubashi University Library).
If references are entirely missing, you can add them using this form.