First-order logic formalisation of Arrow's theorem

Authors:
Umberto Grandi;Ulle Endriss
Affiliations:
Institute for Logic, Language and Computation, University of Amsterdam;Institute for Logic, Language and Computation, University of Amsterdam
Venue:
LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
Year:
2009

Citing 2
Cited 3

Reasoning about judgment and preference aggregation

Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Computer-aided proofs of Arrow's and other impossibility theorems

Artificial Intelligence

Automated search for impossibility theorems in social choice theory: ranking sets of objects

Journal of Artificial Intelligence Research
Using Theorema in the formalization of theoretical economics

MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Applications of logic in social choice theory

CLIMA'11 Proceedings of the 12th international conference on Computational logic in multi-agent systems

Quantified Score

Hi-index	0.00

Visualization

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.