Two important criteria for judging the quality of a voting algorithm are strategy-proofness and Condorcet efficiency. While, according to the Gibbard-Satterthwaite theorem, we can expect no voting mechanism to be fully strategy proof, many Condorcet methods are highly susceptible to compromising, burying, and bullet voting. In this paper I propose a new algorithm which I call “Bidirectional Elimination,” a composite of Instant Runoff Voting and the Coombs Method, which offers the benefit of greater resistance to tactical voting while nearly always electing the Condorcet winner when one exists. A sophisticated program was tailor-made and used to test IRV, the Coombs Method, and Bidirectional Elimination on tens of billions of social preference profiles in combinations of up to ten voters and ten candidates. I offer mathematical proofs showing the new algorithm meets the Condorcet criterion for up to 4 voters and N candidates, or M voters and up to 3 candidates; beyond this, program results show Bidirectional Elimination offers a significant advantage over both IRV and Coombs in approaching Condorcet efficiency.
Key Words
Voting, tactical voting, strategy proofness, Condorcet criterion, instant runoff voting, Coombs Method, social choice theory.