Proving Arrow’s theorem by PROLOG
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).
KeywordsSocial welfare function Arrow’s impossibility theorem PROLOG
Unable to display preview. Download preview PDF.
- Arrow, K. J. (1951/1963). Social choice and individual values (2nd ed.). Yale University Press (Originally published by Wiley).Google Scholar
- Clocksin W.F., Mellish C.S. (2003). Programming in prolog: Using the ISO standard (5th ed.). Berlin, SpringerGoogle Scholar
- Hooker J. (2000). Logic-base methods for optimization: Combining optimization and constraint satisfaction. New York, WileyGoogle Scholar
- Indo, K. (2006). Logic programming for modeling social choice, downlodable from URL: http://www.us.kanto-gakuen.ac.jp/indo/wp/mplsc.html.Google Scholar
- Sterling L., Shapiro E. (1994). The art of prolog: Advanced programming (2nd ed.). Cambridge, MA: MITGoogle Scholar
- Takekuma S. (1997). A proof of arrow’s impossibility theorem by MATHEMATICA. Hitotsubashi Journal of Economics 38, 139–148Google Scholar