Towards automatic argumentation about voting rules

International audienceVoting rules aggregate the preferences of a group to make decisions. As multiple reasonable voting rules exist, the ax-iomatic approach has been proposed to exhibit both their merits and paradoxical behaviors. It consists in characterizing a voting rule by a set of understandable properties called axioms. It is however a difficult task to characterize a voting rule by such axioms, and even when a proof exists, it may be difficult to understand why a specific voting rule fails to satisfy a given axiom, especially for untrained users. In this article, we present an automatic method which determines whether a given rule satisfies a set of axioms. When the rule does not satisfy an axiom, the automatic prover generates comprehensible evidence of the violation in the form of a counterexample. It can be used by non-expert users to comprehend the violation and may serve to argue in favor of other rules which satisfy the axiom. Our method is based on the software analysis technique bounded model checking, which enables bounded verification for properties of software programs. It translates the program together with user-annotations into a reachability problem for those profiles and outcomes which adhere to our specification. The method can be applied to arbitrary voting rules; we demonstrate it on the case of the Borda axiomatization and compare the Borda rule to both the Black and the Copeland voting rules