A theory is developed to explain all positional voting outcomes that can result from a single but arbitrarily chosen profile. This includes all outcomes, paradoxes, and disagreements among positional procedure outcomes as well as all discrepancies in rankings as candidates are dropped or added....

Beyond determining whether procedures can be manipulated, the real goal for any analysis of "strategic behavior" is to identify all settings where and when this can be done, who can do it, and what they should do. By applying the geometric approach of Saari [7, 8] to the Kemeny's Rule (KR), we...

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...

It is shown how bordered hessians, sufficient statistics, and integrability conditions from utility theory are closely related to the characterization theorems for mechanism design. Then, new results are outlined about a theory for implicitly defined objective functions, about how to incorporate...

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...