Journal of Automated Reasoning

, Volume 43, Issue 3, pp 289–304 | Cite as

Social Choice Theory in HOL

Arrow and Gibbard-Satterthwaite
Article

Abstract

This article presents formalizations in higher-order logic of two proofs of Arrow’s impossibility theorem due to Geanakoplos. The Gibbard-Satterthwaite theorem is derived as a corollary. Lacunae found in the literature are discussed.

Keywords

Social choice theory Arrow’s theorem Gibbard-Satterthwaite theorem Higher-order logic Theorem proving 

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References

  1. 1.
    Arrow, K.: A difficulty in the concept of social welfare. J. Polit. Econ. 58, 328–346 (1950)CrossRefGoogle Scholar
  2. 2.
    Arrow, K.: Social Choice and Individual Values. Yale University Press, New Haven (1951)MATHGoogle Scholar
  3. 3.
    Gammie, P.: Some classical results in social choice theory. In: Klein, G., Nipkow, T., Paulson, L. (eds.) The Archive of Formal Proofs. Formal Proof Development. http://afp.sf.net/entries/SenSocialChoice.shtml (2008)
  4. 4.
    Geanakoplos, J.: Three brief proofs of Arrow’s impossibility theorem. Technical report, Cowles Foundation Discussion Paper No. 1123RRR (2001)Google Scholar
  5. 5.
    Geanakoplos, J.: Three brief proofs of Arrow’s impossibility theorem. Econ. Theory 26, 211–215 (2005)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41, 587–601 (1973)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Nipkow, T., Paulson, L., Wenzel, M.: Isabelle/HOL—a Proof Assistant for Higher-Order Logic. Lecture Notes in Computer Science, vol. 2283. Springer, New York (2002)MATHGoogle Scholar
  8. 8.
    Nisan, N.: Introduction to mechanism design (for computer scientists). In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)Google Scholar
  9. 9.
    Reny, P.: Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach. Econ. Lett. 70, 99–105 (2001)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Routley, R.: Repairing proofs of Arrow’s general impossibility theorem and enlarging the scope of the theorem. Notre Dame J. Form. Log. 20, 879–890 (1979)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Satterthwaite, M.: Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theory 10, 187–217 (1975)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Sen, A.: Collective Choice and Social Welfare. Holden-Day, San Francisco (1970)MATHGoogle Scholar
  13. 13.
    Taylor, A.D.: Social Choice and the Mathematics of Manipulation. Cambridge University Press, Cambridge (2005)MATHGoogle Scholar
  14. 14.
    Wiedijk, F.: Arrow’s impossibility theorem. Formaliz. Math. 15, 171–174 (2007)CrossRefGoogle Scholar
  15. 15.
    Wiedijk, F.: Formalizing Arrow’s theorem. Sadhana 34, 193–220 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany

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