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An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set

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Abstract

The lexicographic maximin extension of an ordering is an important and widely used tool in social choice theory. We provide an axiomatization of it by means of five axioms. When the basic ordering is linear the following four (independent) axioms are sufficient: (1) Gärdenfors principle; (2) Neutrality; (3) Strong Fishburn monotonicity; and (4) Extension. Our result may also have applications in the theory of individual choice under uncertainty.

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References

  1. Arrow KJ, Hurwicz L (1972) An optimality criterion for decision-making under ignorance. In: Carter CF, Ford JL (eds) Uncertainty and expectations in economics. Augustus M. Kelley, Fairfield, NJ

    Google Scholar 

  2. Barbera S (1977) The manipulation of social choice mechanisms that do not leave too much to chance. Econometrica 45: 1573–1588

    Google Scholar 

  3. Barbera S, Pattanaik PK Extending an order on a set to the power set: Some remarks on Kannai and Peleg's approach. (mimeograph, 1982); J Econ Theory (unknown)

  4. Fishburn PC (1972) Even-chance lotteries in social choice theory Theory Decision 3: 18–40

    Google Scholar 

  5. Fishburn PC (1981) Comments on the Kannai-Peleg impossibility theorem for extending orders. (mimeograph, 1981); J Econ Theory (unknown)

  6. Gardenfors P (1976) Manipulation of social choice functions. J Econ Theory 13: 217–228

    Google Scholar 

  7. Gardenfors P (1979) On definitions of manipulation of social choice functions. In: Laffont J-J (ed) Aggregation and revelation of preferences. North-Holland, Amsterdam

    Google Scholar 

  8. Heiner R, Packard DJ (1982) A uniqueness result for extending orders; with application to collective choice as inconsistency resolution. (mimeograph, 1982); J Econ Theory (unknown)

  9. Kannai Y, Peleg B A note on the extension of an order on a set to the power set, (mimeograph, 1981); J Econ Theory (unknown)

  10. Kelly J (1977) Strategy-proofness and social choice functions without single-valuedness. Econometrica 45: 439–446

    Google Scholar 

  11. Krantz D, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement. Wiley, New York

    Google Scholar 

  12. Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York

    Google Scholar 

  13. Milnor J (1954) Games against nature. In: Thrall RM, Coomos CH, Davis RL (eds) Decision processes. Wiley, New York

    Google Scholar 

  14. Packard DJ (1979) Preference relations. J Math Psychol 19: 295–306

    Google Scholar 

  15. Packard DJ (1981) Plausibility orderings and social choice. Synthese 49: 415–418

    Google Scholar 

  16. Pattanaik PK (1978) Strategy and group choice. North-Holland, Amsterdam

    Google Scholar 

  17. Rawls J (1971) Theory of justice. Harvard University Press, Cambridge, MA

    Google Scholar 

  18. Rescher N (1976) Plausible reasoning. Van Gorcum, Assen/Amsterdam

    Google Scholar 

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Author notes

  1. P. K. Pattanaik

    Present address: Department of Economics, University of Birmingham, B15 2TT, Birmingham, United Kingdom

  2. B. Peleg

    Present address: Department of Mathematics, The Hebrew University, 91904, Jerusalem, Israel

Authors and Affiliations

  1. The Institute for Advanced Studies, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel

    P. K. Pattanaik & B. Peleg

Authors
  1. P. K. Pattanaik
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  2. B. Peleg
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Pattanaik, P.K., Peleg, B. An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set. Soc Choice Welfare 1, 113–122 (1984). https://doi.org/10.1007/BF00452883

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  • DOI: https://doi.org/10.1007/BF00452883

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