Paradoxes from statistics and decision sciences form amusing, yet intriguing mathematical puzzles. On deeper examination, they constitute serious problems that could cause us, unintentionally, to adopt inferior alternatives. It is indicated here how ideas form "dynamical chaos" and orbits of...

A central political and decision science issue is to understand how election outcomes can change with the choice of a procedure or the slate of candidates. These questions are answered for the important Copeland method (CM) where, with a geometric approach, we characterize all relationships...

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 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....

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...

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...