PP-2009-40: First-Order Logic Formalisation of Arrow's Theorem

PP-2009-40: Grandi, Umberto and Endriss, Ulle (2009) First-Order Logic Formalisation of Arrow's Theorem. [Report]

[img]
Preview
Text (Full Text)
PP-2009-40.text.pdf

Download (205kB) | Preview
[img] Text (Abstract)
PP-2009-40.abstract.txt

Download (915B)

Abstract

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.

Item Type: Report
Report Nr: PP-2009-40
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: social choice theory; computational social choice; automated reasoning
Subjects: Computation
Depositing User: Ulle Endriss
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/370

Actions (login required)

View Item View Item