Computational Economics

, Volume 30, Issue 1, pp 57–63 | Cite as

Proving Arrow’s theorem by PROLOG

  • Kenryo IndoEmail author


This paper presented a simple PROLOG implementation for Arrow’s Social welfare function (SWF). Arrow (Social choice and individual values, Yale University Press, 1963) proved that any SWF which satisfies a set of conditions IIA, Pareto, and unrestricted domain should be dictatorial. The PROLOG program can prove the theorem for 3-alternative 2-agent case. With a minor modification it proves a version of the theorem without the Pareto condition by Wilson (Journal of Economic Theory, 5, 478–486, 1972).


Social welfare function Arrow’s impossibility theorem PROLOG 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arrow, K. J. (1951/1963). Social choice and individual values (2nd ed.). Yale University Press (Originally published by Wiley).Google Scholar
  2. Clocksin W.F., Mellish C.S. (2003). Programming in prolog: Using the ISO standard (5th ed.). Berlin, SpringerGoogle Scholar
  3. Hooker J. (2000). Logic-base methods for optimization: Combining optimization and constraint satisfaction. New York, WileyGoogle Scholar
  4. Indo, K. (2006). Logic programming for modeling social choice, downlodable from URL: Scholar
  5. Nisan N., Ronen A. (2001). Algorithmic mechanism design. Games and Economic Behavior 35, 166–196CrossRefGoogle Scholar
  6. Robinson A. (1965). A machine-oriented logic based on the resolution principle. JACM 12(1): 23–41CrossRefGoogle Scholar
  7. Sterling L., Shapiro E. (1994). The art of prolog: Advanced programming (2nd ed.). Cambridge, MA: MITGoogle Scholar
  8. Takekuma S. (1997). A proof of arrow’s impossibility theorem by MATHEMATICA. Hitotsubashi Journal of Economics 38, 139–148Google Scholar
  9. Wilson R. (1972). Social choice theory without the Pareto principle. Journal of Economic Theory 5, 478–486CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.EconomicsKanto Gakuen UniversityOtaJapan

Personalised recommendations