An important issue for economics and the decision sciences is to understand why allocation and decision procedures are plagued by manipulative and paradoxical behavior once there are n3 or n=3 alternatives. Valuable insight is obtained by exploiting the relative simplicity of the widely used...

A theory is developed to explain all possible positional voting paradoxes coming from a single but arbitraily chosen profile. This includes all pairwise voting cycles, all conflict between Borda and Condorcet winners and rankings, all disagreement in outcomes among positional procedures, and all...

A q-rule is where, for n-voters, a winning coalition consists of q or more voters. An important question is to determine when, generically, core points exist; that is, when the core exists in other than highly contrived settings. As known, the answer depends upon the dimension of issue space....

By changing the choice of a positional voting method, different election rankings can results from a fixed profile. A geometric theory is developed to explain why this occurs, to completely characterize all possible sets of rankings that can arise in this manner, to determine the number of...