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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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  • 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.
    • Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1770-1782
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    2. Matsuki, Jun & Tadenuma, Koichi & 蓼沼, 宏一, 2013. "Choice via Grouping Procedures," Discussion Papers 2013-08, Graduate School of Economics, Hitotsubashi University.
    3. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    4. Renou, Ludovic & Schlag, Karl H., 2014. "Ordients: Optimization and comparative statics without utility functions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 612-632.
    5. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
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    8. Sakamoto, Norihito, 2020. "Equity Principles and Interpersonal Comparison of Well-being: Old and New Joint Characterizations of Generalized Leximin, Rank-dependent Utilitarian, and Leximin Rules," RCNE Discussion Paper Series 7, Research Center for Normative Economics, Institute of Economic Research, Hitotsubashi University.
    9. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
    10. Yu‐Lin Hsu & Gavin C. Reid, 2021. "Two‐stage decision‐making within the firm: Analysis and case studies," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(6), pages 1355-1373, September.
    11. C. Binder, 2014. "Plural identities and preference formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 959-976, April.
    12. Christopher Kops, 2018. "(F)Lexicographic shortlist method," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 79-97, January.
    13. Rohan Dutta & Sean Horan, 2015. "Inferring Rationales from Choice: Identification for Rational Shortlist Methods," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 179-201, November.
    14. 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.
    15. Nikolai Hoberg & Stefan Baumgärtner, 2014. "Value pluralism, trade-offs and efficiencies," Working Paper Series in Economics 311, University of Lüneburg, Institute of Economics.
    16. Salvador Barberà & Alejandro Neme, 2015. "Ordinal Relative Satisficing Behavior: Theory and Experiments," Working Papers 790, Barcelona School of Economics.
    17. Battal Doğan & Kemal Yildiz, 2023. "Choice with Affirmative Action," Management Science, INFORMS, vol. 69(4), pages 2284-2296, April.
    18. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    19. Lleras, Juan Sebastián & Masatlioglu, Yusufcan & Nakajima, Daisuke & Ozbay, Erkut Y., 2017. "When more is less: Limited consideration," Journal of Economic Theory, Elsevier, vol. 170(C), pages 70-85.
    20. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    21. Yu-Lin Hsu & Gavin C. Reid, 2021. "A Two-Stage Model of Decision-Making over Financial Reporting Regimes and Techniques: Analysis and UK Case Studies," Working Papers wp529, Centre for Business Research, University of Cambridge.
    22. Ludovic Renou & Karl H. Schlag, 2009. "From Ordients to Optimization: Substitution Effects without Differentiability," Discussion Papers in Economics 09/6, Division of Economics, School of Business, University of Leicester.
    23. Michael Mandler, 2021. "The lexicographic method in preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 553-577, March.
    24. Cherepanov, Vadim & Feddersen, Timothy & ,, 2013. "Rationalization," Theoretical Economics, Econometric Society, vol. 8(3), September.

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    More about this item

    Keywords

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

    JEL classification:

    • 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; Revolutions

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