Explaining All Three-Alternative Voting Outcomes

A theory is developed to explain all possible three-alternative (single-profile) pairwise and positional voting outcomes. This includes all preference aggregation paradoxes, cycles, conflict between the Borda and Condorcet winners, differences among positional outcomes (e.g., the plurality and antiplurality methods), and differences among procedures using these outcomes (e.g., runoffs, Kemeny's rule, and Copeland's method). It is shown how to identify, interpret, and construct all profiles supporting each paradox. Among new conclusions, it is shown why a standard for the field, the Condorcet winner, is seriously flawed. Journal of Economic Literature Classification Numbers: D72, D71. 1999 Academic Press