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International Symposium on Frontiers of Combining Systems

FroCoS 2019: Frontiers of Combining Systems pp 240–256Cite as

Verifying Randomised Social Choice

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11715))

Abstract

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.

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Notes

  1. 1.

    The meaning of these concepts will be made more precise later – in particular, what it means for an agent to prefer one lottery over another.

  2. 2.

    Readers who are used to systems like Coq or Lean might wonder why one does not simply use the entire types \(\nu \) and \(\gamma \). The reason for this is that we sometimes want to decrease or increase the number of agents and alternatives. Doing this without explicit carrier sets can be problematic in Isabelle.

  3. 3.

    Except for oracles, which I do not use here.

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Acknowledgments

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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Authors and Affiliations

  1. Technische Universität Mänchen, 85748, Garching bei München, Germany

    Manuel Eberl

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  1. Manuel Eberl
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Correspondence to Manuel Eberl .

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Editors and Affiliations

  1. CNRS, University of Toulouse, Toulouse, France

    Andreas Herzig

  2. Middlesex University London, London, UK

    Andrei Popescu

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Eberl, M. (2019). Verifying Randomised Social Choice. In: Herzig, A., Popescu, A. (eds) Frontiers of Combining Systems. FroCoS 2019. Lecture Notes in Computer Science(), vol 11715. Springer, Cham. https://doi.org/10.1007/978-3-030-29007-8_14

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  • DOI: https://doi.org/10.1007/978-3-030-29007-8_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29006-1

  • Online ISBN: 978-3-030-29007-8

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