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 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...

This is the first of three papers introducing a theory for positional voting methods that determines all possible election rankings and relationships that ever could occur with a profile over all possible subsets of candidates for any specified choices of positional voting methods. As such,...

It is shown how simple geometry can be used to analyze and discover new properties about pairwise and positional voting rules as well as for those rules (e.g., runoffs and Approval Voting) that rely on these methods. The description starts by providing a geometric way to depict profiles, which...

To efficiently realize a specified goal in a distributive fashion, there needs to be an appropriate "division of labor." This is true for distributive algorithms that take advantage of the concurrent features of the new generation of computers. This is true in the design of a complex...

General conclusions relating pairwise tallies with positional (e.g., plurality, antiplurality (“vote-for-two”)) election outcomes were previously known only for the Borda Count. While it has been known since the eighteenth century that the Borda and Condorcet winners need not agree, it had...

Cycles, empty cores, intransitivities, and other complexities affect group decision and voting rules. Approaches that prevent these difficulties include the Nakamura number, Greenberg’s theorem, and single peaked preferences. The results derived here subsume and significantly extend these...

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