Voting Theory
Strategy-Proofness, Independence of Irrelevant Alternatives, and Majority Rule
Partha Dasgupta and Eric Maskin show that among all possible voting methods, majority rule—as used in Consensus Choice Voting—is uniquely able to satisfy a set of fundamental fairness principles, including strategy-proofness (resisting manipulation), anonymity, and independence from irrelevant alternatives, as long as majority preferences do not form cycles. The authors provide both theoretical and real-world evidence that Condorcet winners (Consensus Choices) usually exist in elections and that majority rule avoids the vote-splitting problems common in systems like plurality or runoff voting. The implications of their findings are that Consensus Choice Voting is a robust, fair, and manipulation-resistant system that reflects true majority preferences and encourages candidate accountability.
Characterizations of voting rules based on majority margins
Yifeng Ding, Wesley H. Holliday, and Eric Pacuit introduce and analyze a critical fairness principle called Preferential Equality, which ensures that if either of the two voters switch their rankings between two adjacent candidates, the impact on the election outcome should be the same regardless of which voter makes the switch. This principle guarantees that all voters' preferences are treated equally in head-to-head candidate comparisons, preventing distortions where some voters' changes have greater influence than others. The study also compares margin-based rules with other voting methods, such as Instant Runoff Voting (IRV), showing that IRV can violate Preferential Equality by producing different outcomes depending on which voters shift their rankings. By identifying and formalizing the normative foundations of margin-based rules, Ding, Holliday and Pacuit provide a framework for evaluating voting systems based on fairness, consistency, and the equal treatment of voter preferences.
An extension of May’s Theorem to three alternatives: axiomatizing Minimax voting
Wesley H. Holliday and Eric Pacuit extend May's theorem, originally formulated for two-alternative elections, to elections involving three alternatives. May’s axioms include requirements such as neutrality (treating candidates equally), anonymity (treating voters equally), and positive responsiveness (candidates benefiting from rising in voter rankings). Holliday and Pacuit propose additional fairness axioms designed to mitigate spoiler effects and eliminate the so-called strong no-show paradox. Through these axioms, they show that Minimax voting, which selects the candidate with the smallest maximum defeat in pairwise matchups, uniquely satisfies their criteria for three-candidate elections. They argue that this extension helps address the complexities introduced when more than two alternatives are involved, providing an axiomatic basis for selecting a fair and rational voting method.
The Social Utility of Voting Revisited
Wesley H. Holliday and Eric Pacuit revisit foundational questions about how well various voting methods come to electing candidates who maximize the utility of voters, using updated spatial modeling and modern computational power. They find that from the perspective of Utilitarianism, the best methods overall are certain Condorcet methods, while from the perspective of so-called Relative Utilitarianism, the best method overall is the Borda count—though in either case the best Condorcet methods and the Borda count are close in performance. Significantly behind these methods in social utility is Instant Runoff Voting, followed by Plurality voting as the worst method (at least among deterministic methods) that they studied. Their findings suggest that adopting Consensus Choice Voting could lead to significantly fairer, more representative outcomes and help address voter dissatisfaction with current voting systems.