New Research: A Simple Voting Method for Final Four and Final Five Elections
Building on previous work, Wesley H. Holliday introduces a simple voting method for Final Four elections and extends it to Final Five elections. Most Wins, Smallest Loss (MWSL) is a Condorcet-consistent voting method defined as follows:
Determine the number of head-to-head wins for each candidate.
The candidate with the most wins is elected.
If multiple candidates tie for the most wins, then elect the one with the smallest head-to-head loss.
A rationale for MWSL is that it picks the candidate who is closest to being a Condorcet winner, when it is clear who that candidate is. According to Holliday, “among the candidates tied for the most wins, the one with the smallest loss is closest to being an outright winner based on their number of wins, since all it would take is flipping that small loss.” This reflects a common intuition in competitive settings, namely that a team that was closer to being undefeated is more deserving than one whose loss was more decisive. Another justification is simplicity and transparency. The method can be explained without invoking complex concepts like cycles or iterative elimination. In short, voters and journalists can more easily understand what it means: “Count each candidate’s wins. If there’s a tie, see who had the smallest loss.”
For Final Four elections, MWSL is uniquely characterized by the following axioms, informally stated:
Proximity to Condorcet: if one candidate can be made the Condorcet winner by improving one of their head-to-head margins by a certain number of votes, while another candidate cannot be made the Condorcet winner by improving all of their margins by the same number of voters, then the second candidate—who is further from being the Condorcet winner—should not be elected;
Independence of Irrelevant Defeats: the winner cannot change from one candidate to another as a result of changing a margin of victory between some other two candidates;
Win Monotonicity: if one of the winner’s margins of victory increases by the same amount as another candidate’s margin of victory (against a third candidate), the winner remains the same;
Win Dominance: if candidate A defeats B and every candidate that B defeats (by at least as much), then B cannot win;
Rare Ties: assuming all pairwise margins are distinct, the method selects a unique winner.
For Final Five elections, the axiomatization replaces Proximity to Condorcet with Proximity to Copeland—which simply replaces ‘Condorcet winner’ with 'unique Copeland winner', i.e., a candidate with more wins than any other—and adds Immunity to Spoilers, which says that if a candidate A would win without B in the election, and A would beat B head-to-head, then adding B to the election cannot cause a third candidate C to win. In Final Five elections, MWSL still has the same simple tie-breaking rule: among candidates tied for the most wins, elect the one with the smallest loss.
