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An alternative proof of Fishburn’s axiomatization of lexicographic preferences

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  • Mitra, Manipushpak
  • Sen, Debapriya

Abstract

We present an alternative proof of Fishburn’s (1975) axiomatization of lexicographic preferences. The essence of our proof lies in identifying “an extremely pivotal factor”. Our proof reconfirms the strong interconnections between Arrow’s and Gibbard–Satterthwaite’s theorems with Fishburn’s axiomatization.

Suggested Citation

  • Mitra, Manipushpak & Sen, Debapriya, 2014. "An alternative proof of Fishburn’s axiomatization of lexicographic preferences," Economics Letters, Elsevier, vol. 124(2), pages 168-170.
    • Handle: RePEc:eee:ecolet:v:124:y:2014:i:2:p:168-170
    DOI: 10.1016/j.econlet.2014.05.011
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    References listed on IDEAS

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    1. Barbara, Salvador & Jackson, Matthew, 1988. "Maximin, leximin, and the protective criterion: Characterizations and comparisons," Journal of Economic Theory, Elsevier, vol. 46(1), pages 34-44, October.
    2. Knoblauch, Vicki, 2005. "Continuous lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 812-825, November.
    3. Peter C. Fishburn, 1975. "Axioms for Lexicographic Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 415-419.
    4. Charles R. Plott & James T. Little & Robert P. Parks, 1975. "Individual Choice when Objects have "Ordinal" Properties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 403-413.
    5. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    6. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    7. Hougaard, Jens Leth & Tvede, Mich, 2001. "The existence of maximal elements: generalized lexicographic relations," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 111-115, November.
    8. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, July.
    9. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    11. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
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    Cited by:

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    2. Petri, Henrik & Voorneveld, Mark, 2016. "Characterizing lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 54-61.
    3. Mridu Prabal Goswami & Manipushpak Mitra & Debapriya Sen, 2022. "A Characterization of Lexicographic Preferences," Decision Analysis, INFORMS, vol. 19(2), pages 170-187, June.
    4. Kuntal Banerjee, 2018. "On the Representability of a Class of Lexicographic Preferences," Economics Bulletin, AccessEcon, vol. 38(2), pages 1213-1218.

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    More about this item

    Keywords

    Axiomatization; Lexicographic preference; Extremely pivotal factor;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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