We consider the Copeland voting rule, a classical and simple voting rule that takes a set of voters’ rankings over a set of candidates and outputs the candidate that wins the most pair-wise match-ups against other candidates. We examine Copeland in the metric distortion model of voting, with a focus on low-dimensional spaces. We show that Copeland voting on the line metric has a metric distortion of 3, which is a lower metric distortion than its ratio of 5 for general metrics, and also better than the distortion on the line of other common voting rules like Plurality and Borda. It is also lower than the best-known bound for STV, known to the general public as “Ranked Choice Voting” (RCV), which is increasingly being adopted by state and local governments in the United States. We then run simulations in which randomly generated voters and candidates are placed in a Euclidean space. For each random trial, we compare the Copeland rule to Plurality, Borda, Single Transferable Vote (STV/RCV), and Plurality Veto, the novel rule recently proposed that achieves the best possible metric distortion of 3 for general metrics. We show in our empirical study that the Copeland rule outperforms all others, including Plurality Veto and STV/RCV, with respect to distortion as well as the rate at which the optimal candidate is elected. We also test the same voting rules for the satisfaction rate of desirable criteria, such as the Independence of Irrelevant Alternatives, and in these respects, Copeland still outperforms the other voting rules.

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A Case for Copeland: from Theory to Practice

  • Michelle Le,
  • Chloe Nguyen,
  • Leo Claney,
  • Krishh Tipnis,
  • Brian MacSweeney,
  • Eric Huber,
  • Christine Chung

摘要

We consider the Copeland voting rule, a classical and simple voting rule that takes a set of voters’ rankings over a set of candidates and outputs the candidate that wins the most pair-wise match-ups against other candidates. We examine Copeland in the metric distortion model of voting, with a focus on low-dimensional spaces. We show that Copeland voting on the line metric has a metric distortion of 3, which is a lower metric distortion than its ratio of 5 for general metrics, and also better than the distortion on the line of other common voting rules like Plurality and Borda. It is also lower than the best-known bound for STV, known to the general public as “Ranked Choice Voting” (RCV), which is increasingly being adopted by state and local governments in the United States. We then run simulations in which randomly generated voters and candidates are placed in a Euclidean space. For each random trial, we compare the Copeland rule to Plurality, Borda, Single Transferable Vote (STV/RCV), and Plurality Veto, the novel rule recently proposed that achieves the best possible metric distortion of 3 for general metrics. We show in our empirical study that the Copeland rule outperforms all others, including Plurality Veto and STV/RCV, with respect to distortion as well as the rate at which the optimal candidate is elected. We also test the same voting rules for the satisfaction rate of desirable criteria, such as the Independence of Irrelevant Alternatives, and in these respects, Copeland still outperforms the other voting rules.