First-Order Logic Formalisation of Arrow’s Theorem

  • Umberto Grandi
  • Ulle Endriss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5834)


Arrow’s Theorem is a central result in social choice theory. It states that, under certain natural conditions, it is impossible to aggregate the preferences of a finite set of individuals into a social preference ordering. We formalise this result in the language of first-order logic, thereby reducing Arrow’s Theorem to a statement saying that a given set of first-order formulas does not possess a finite model. In the long run, we hope that this formalisation can serve as the basis for a fully automated proof of Arrow’s Theorem and similar results in social choice theory. We prove that this is possible in principle, at least for a fixed number of individuals, and we report on initial experiments with automated reasoning tools.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Umberto Grandi
    • 1
  • Ulle Endriss
    • 1
  1. 1.Institute for Logic, Language and ComputationUniversity of Amsterdamthe Netherlands

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