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Choice under complete uncertainty: axiomatic characterizations of some decision rules

Author

Listed:
  • Prasanta K. Pattanaik

    () (Department of Economics, University of California, Riverside, CA 92521, USA)

  • Yongsheng Xu

    () (Department of Economics, Andrew Young School of Economics, Georgia State University,Atlanta, GA 30303, USA)

  • Walter Bossert

    () (Department of Economics, University of Nottingham, Nottingham NG7 2RD, UK)

Abstract

We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules.

Suggested Citation

  • Prasanta K. Pattanaik & Yongsheng Xu & Walter Bossert, 2000. "Choice under complete uncertainty: axiomatic characterizations of some decision rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 295-312.
  • Handle: RePEc:spr:joecth:v:16:y:2000:i:2:p:295-312
    Note: Received: August 20, 1998; revised version: November 3, 1999
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    Citations

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    Cited by:

    1. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 729-741, October.
    2. Vázquez, Carmen, 2014. "Ranking opportunity sets on the basis of similarities of preferences: A proposal," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 23-26.
    3. José Alcantud & Ritxar Arlegi, 2008. "Ranking sets additively in decisional contexts: an axiomatic characterization," Theory and Decision, Springer, vol. 64(2), pages 147-171, March.
    4. Arlegi, Ritxar & Dimitrov, Dinko, 2016. "Power set extensions of dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 20-29.
    5. Ran Spiegler, 2001. "Inferring a linear ordering over a power set," Theory and Decision, Springer, vol. 51(1), pages 31-49, August.
    6. Shin Sato, 2008. "On strategy-proof social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 331-343, August.
    7. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Sebastian Bervoets, 2010. "An axiomatic approach to predictability of outcomes in an interactive setting," Theory and Decision, Springer, vol. 68(3), pages 311-323, March.
    9. Ritxar Arlegi, 2001. "Rational Evaluation of Actions Under Complete Uncertainty," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0114, Departamento de Economía - Universidad Pública de Navarra.
    10. Murat Sertel & Arkadii Slinko, 2007. "Ranking committees, income streams or multisets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(2), pages 265-287, February.
    11. Jorge Alcalde-Unzu & Ricardo Arlegi & Miguel Ballester, 2013. "Uncertainty with ordinal likelihood information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 397-425, July.
    12. Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
    13. Guerdjikova, Ani, 2006. "Portfolio Choice and Asset Prices in an Economy Populated by Case-Based Decision Makers," Working Papers 06-13, Cornell University, Center for Analytic Economics.
    14. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 227-245, March.
    15. Amélie Vrijdags, 2010. "An experimental investigation of transitivity in set ranking," Theory and Decision, Springer, vol. 68(1), pages 213-232, February.
    16. Carmelo Rodríguez-Álvarez, 2009. "On strategy-proof social choice correspondences: a comment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 29-35, January.
    17. Ritxar Arlegi, 2002. "A Note on Bossert, Pattanaik and Xu’s “Choice Under Complete Uncertainty: Axiomatic Characterization of Some Decision Rules”," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0202, Departamento de Economía - Universidad Pública de Navarra.
    18. BOSSERT, Walter & SLINKO, Arkadii, 2004. "Relative Uncertainty and Additively Representable Set Rankings," Cahiers de recherche 2004-13, Universite de Montreal, Departement de sciences economiques.
    19. Kerber, Manfred & Lange, Christoph & Rowat, Colin, 2016. "An introduction to mechanized reasoning," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 26-39.
    20. Gekker, Ruvin & van Hees, Martin, 2006. "Freedom, opportunity and uncertainty: A logical approach," Journal of Economic Theory, Elsevier, vol. 130(1), pages 246-263, September.

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