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Lexicographic Compositions of Multiple Criteria for Decision Making

Author

Listed:
  • Houy, Nicolas
  • Tadenuma, Koichi
  • 蓼沼, 宏一

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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Suggested Citation

  • Houy, Nicolas & Tadenuma, Koichi & 蓼沼, 宏一, 2007. "Lexicographic Compositions of Multiple Criteria for Decision Making," Discussion Papers 2007-13, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2007-13
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    File URL: https://hit-u.repo.nii.ac.jp/record/2052350/files/070econDP07-13.pdf
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    Cited by:

    1. Battal Doğan & Serhat Doğan & Kemal Yıldız, 2021. "Lexicographic choice under variable capacity constraints," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(1), pages 172-196, February.
    2. 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.
    3. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    4. Matsuki, Jun & Tadenuma, Koichi & 蓼沼, 宏一, 2013. "Choice via Grouping Procedures," CCES Discussion Paper Series 52, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    5. Debasis Mishra & Kolagani Paramahamsa, 2018. "Selling to a naive agent with two rationales," Discussion Papers 18-03, Indian Statistical Institute, Delhi.
    6. Nikolai Hoberg & Stefan Baumgärtner, 2014. "Value pluralism, trade-offs and efficiencies," Working Paper Series in Economics 311, University of Lüneburg, Institute of Economics.
    7. Cherepanov, Vadim & Feddersen, Timothy & ,, 2013. "Rationalization," Theoretical Economics, Econometric Society, vol. 8(3), September.
    8. 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.
    9. 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.
    10. Salvador Barberà & Alejandro Neme, 2015. "Ordinal Relative Satisficing Behavior: Theory and Experiments," Working Papers 790, Barcelona School of Economics.
    11. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    12. 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.
    13. 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.
    14. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
    15. 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.
    16. 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.
    17. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    18. Battal Doğan & Kemal Yildiz, 2023. "Choice with Affirmative Action," Management Science, INFORMS, vol. 69(4), pages 2284-2296, April.
    19. 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.
    20. 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.
    21. 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.
    22. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    23. Mandler, Michael, 2015. "Rational agents are the quickest," Journal of Economic Theory, Elsevier, vol. 155(C), pages 206-233.
    24. 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.

    More about this item

    Keywords

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    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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