Verifying Randomised Social Choice
This work describes the formalisation of a recent result from Randomised Social Choice Theory in Isabelle/HOL. The original result had been obtained through the use of linear programming, an unverified Java program, and SMT solvers; at the time that the formalisation effort began, no human-readable proof was available. Thus, the formalisation with Isabelle eventually served as both independent rigorous confirmation of the original result and led to human-readable proofs both in Isabelle and on paper.
This presentation focuses on the process of the formalisation itself, the domain-specific tooling that was developed for it in Isabelle, and how the structured human-readable proof was constructed from the SMT proof. It also briefly discusses how the formalisation uncovered a serious flaw in a second peer-reviewed publication.
I would like to thank Florian Brandl, Felix Brandt, and Christian Geist for bringing the field of randomised Social Choice to my attention as a target for formalisation, and for their continued assistance. I also thank Florian Brandl and Felix Brandt for commenting on a draft of this document. I also thank the anonymous reviewers for their comments.
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