VERICONDOR: End-to-End Verifiable Condorcet Voting with support for Strict Preference and Indifference

Abstract

Condorcet voting is widely regarded as one of the most important voting systems in social choice theory. However, it has seen little adoption in practice, due to complex tallying and the need to break ties when there is a Condorcet cycle. Several online Condorcet voting systems have been developed to perform digital tallying and tie-breaking procedures, but they require voters to completely trust the server. Additionally, many end-to-end (E2E) verifiable e-voting systems require trustworthy authorities to perform complex decryption and tallying operations. We propose VERICONDOR, the first E2E verifiable Condorcet e-voting system without tallying authorities. VERICONDOR allows a voter to fully verify the tallying integrity by themselves while providing strong protection of ballot secrecy. We present novel zero-knowledge proof techniques to prove the well-formedness of an encrypted ballot with exceptional efficiency. VERICONDOR supports ranking candidates with strict preference, as well as indifference. The computational cost is exceptionally efficient for strict preferences at \(\mathcal{O}(n^{2})\) per ballot for \(n\) candidates, whilst remaining practical for indifferences at \(\mathcal{O}(n^{3})\) . In the case of ties, we show how to apply known Condorcet methods to break them in a publicly verifiable manner. Finally, we present a proof of concept implementation and evaluate its performance.