As shown, the source of Sen's and Arrow's impossibility theorems is that Sen's Liberal condition and Arrow's IIA counter the critical assumption that voters' have transitive preferences. As this allows transitive and certain cyclic preferences to become indistinguishable, the Pareto condition...

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...