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A simple Condorcet voting method for Final Four elections
Wesley H. Holliday introduces a simple form of Consensus Choice Voting specifically designed for elections involving up to four candidates ("Final Four elections"). In this method, voters rank candidates in order of preference. If one candidate wins all head-to-head matchups against the others, that candidate wins outright. If no candidate achieves this, the candidate who loses only one matchup by the smallest margin of votes wins. The method is designed to be simple and clear to voters, avoiding common issues such as complexity and opacity found in other ranked-choice methods like Instant Runoff Voting (IRV). This method guarantees the election of a broadly preferred candidate, preventing scenarios like the election of Condorcet losers (those who lose every head-to-head matchup), and promoting fairness, stability, and representative outcomes.
Four Condorcet-Hare Hybrid Methods for Single-Winner Elections
James Green-Armytage shows that the concept of majority rule is trickier than most people realize. When there are only two candidates in an election, then its meaning is quite clear: it tells us that the candidate with the most votes is elected. However, when there are more than two candidates, and no single candidate is the first choice of a majority, the meaning is no longer obvious. The Condorcet principle offers a plausible guideline for the meaning of majority rule in multi-candidate elections: if voters rank candidates in order of preference, and these rankings indicate that there is a candidate who would win a majority of votes in a one-on-one race against any other candidate on the ballot (a Condorcet winner), then we may interpret ‘majority rule’ as requiring his election.
How Should Votes Be Cast and Counted?
In this book chapter, Nicolaus Tideman evaluates 18 voting rules using both logical and statistical criteria—focusing on how often a rule selects the most broadly supported candidate, resists strategic manipulation, and avoids ties. Tideman highlights Condorcet-Hare, a version of Consensus Choice Voting, as the most balanced method, offering high sincere efficiency, excellent resistance to strategy, and clone independence, while maintaining acceptable simplicity. The evidence supports the potential of Consensus Choice Voting as a fair and robust method for ensuring voter equality, reducing polarization, and improving the quality of democratic outcomes.
The best Condorcet-compatible election method: Ranked Pairs
Charles Munger Jr. compares different Condorcet-compatible voting methods and concludes that Ranked Pairs is the best choice. Ranked Pairs clearly ranks candidates based on voters’ preferences in head-to-head matchups, selecting the candidate who wins the strongest majority in each pairwise contest. The method is particularly valuable because it is intuitive, straightforward to execute, and immune to manipulation through candidate "cloning"—situations where similar candidates split votes unfairly. Ranked Pairs reliably produces meaningful, consistent outcomes and is simple enough for voters and election officials to understand and verify. This makes it superior to other Condorcet-compatible methods, such as Beatpath, because it better balances fairness, transparency, practicality, and resistance to strategic manipulation.
A Dodgson-Hare Synthesis
James Green-Armytage introduces a new voting method, named "Dodgson-Hare," combining ideas from mathematician Charles Dodgson (also known as Lewis Carroll) and Thomas Hare. Dodgson originally proposed that voters first select a Condorcet winner—someone who beats all others head-to-head. If no such candidate exists (due to cyclical majority preferences), voters would reconsider their choices and vote again. The new Dodgson-Hare method improves on this by allowing candidates outside the Smith set (the smallest set of candidates who beat every candidate outside the set) to be eliminated first, then permitting candidate withdrawal, and finally using Hare's method (eliminating the candidate with fewest first-choice votes) to resolve any remaining cycles. The study finds that Dodgson-Hare significantly reduces the likelihood of strategic voting manipulations compared to other popular methods, particularly in scenarios modeled as ideological spectrums (one-dimensional spaces). The results suggest this method could ensure more honest voting, produce outcomes closer to voters' true preferences, and enhance overall election integrity.