A theory is developed to explain all possible (single profile) positional voting paradoxes. This includes all pairwise voting cycles, problems with agendas, conflict between the Borda and Condorcet winners, and differences among positional outcomes (such as the plurality and antiplurality methods). I show how to construct profiles to illustrate all of these paradoxes. Among the new conclusions contradicting accepted belief is that rather than being a standard for the field, the Condorcet winner has serious flaws. This paper discusses three candidates; the companion paper  handles n is greater to or equal to 3 candidates.