Explaining all three-alternative voting outcomes

A theory is developed to explain all possible three-alternative (single-pro file) pairwise and positional voting outcomes. This includes all preference aggregation paradoxes, cycles, conflict between the Borda and Condorcet wi nners, differences among positional outcomes (e.g., the plurality and antip lurality methods), and differences among procedures using these outcomes (e .g., runoffs, Kemeny's rule, and Copeland's method). It is shown how to ide ntify, interpret, and construct all profiles supporting each paradox. Among new conclusions, it is shown why a standard for the field, the Condorcet w inner, is seriously flawed. (C) 1999 Academic Press.