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Machine-Checked Reasoning About Complex Voting Schemes Using Higher-Order Logic

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E-Voting and Identity (Vote-ID 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9269))

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Abstract

We describe how we first formally encoded the English-language Parliamentary Act for the Hare-Clark Single Transferable Vote-counting scheme used in the Australian state of Tasmania into higher-order logic, producing SPECHOL. Based on this logical specification, we then encoded an SML program to count ballots according to this specification inside the interactive theorem prover HOL4, giving us IMPHOL. We then manually transliterated the program as a real SML program IMP. We are currently verifying that the formalisation of the implementation implies the formalisation of the specification: that is, we are using the HOL4 interactive theorem prover to prove the implication IMPHOL \(\rightarrow \) SPECHOL.

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Notes

  1. 1.

    If a large number of ballots are generated naïvely, they become spread too evenly between the candidates. This results in no candidate being elected until the final stages of the count, which is unrealistic. The candidates were given random popularity ratings to produce uneven distributions of ballots to avoid this issue.

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Acknowledgements

We are extremely grateful to the many suggestions for improvement from the reviewers of VoteID 2015. We have tried to take every comment into account, and have even used some of the suggested prose verbatim.

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Authors and Affiliations

  1. Research School of Computer Science, Australian National University, Canberra, Australia

    Jeremy E. Dawson, Rajeev Goré & Thomas Meumann

Authors
  1. Jeremy E. Dawson
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  2. Rajeev Goré
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  3. Thomas Meumann
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Corresponding author

Correspondence to Rajeev Goré .

Editor information

Editors and Affiliations

  1. Bern University of Applied Sciences, Biel, Switzerland

    Rolf Haenni

  2. Bern University of Applied Sciences, Biel, Switzerland

    Reto E. Koenig

  3. Royal Institute of Technology, Stockholm, Sweden

    Douglas Wikström

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Dawson, J.E., Goré, R., Meumann, T. (2015). Machine-Checked Reasoning About Complex Voting Schemes Using Higher-Order Logic. In: Haenni, R., Koenig, R., Wikström, D. (eds) E-Voting and Identity. Vote-ID 2015. Lecture Notes in Computer Science(), vol 9269. Springer, Cham. https://doi.org/10.1007/978-3-319-22270-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-22270-7_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22269-1

  • Online ISBN: 978-3-319-22270-7

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