Condorcet Methods - When, Why and How?

Geometric representations of 3-candidate profiles are used to investigate properties of preferential election methods. The representation visualizes both the possibility to win by agenda manipulation, i.e. introducing a third and chanceless candidate in a 2-candidate race, and the possibility to win a 3-candidate election through different kinds of strategic voting. Here the focus is on the "burying" strategy in single-winner elections, where the win is obtained by ranking a main competitor artificially low. Condorcet methods are compared with the major alternatives (Borda Count, Approval Voting, Instant Runoff Voting). Various Condorcet methods are studied, and one method is proposed that minimizes the number of noncyclic profiles where burying is possible.Preferential election methods; agenda manipulation; strategic voting

Voces Populi and the Art of Listening

The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s favorite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles allowing this strategy. Theorems 2, 3, and 4 establish conditions for an anonymous and neutral 3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these properties; among the others "conditional IRV" gives the strongest challenge to the plurality winner. Conditional IRV is extended to any number of candidates. Theorem 5 is an impossibility of Gibbard-Satterthwaite type, describing 3 specific strategies that cannot all be avoided in meaningful anonymous and neutral elections.Preferential Election methods; Plurality Election methods