This paper considers electoral competition between two office-motivated parties and one voter, in the presence of two alternative policies and under imperfect information. The theory of refinements of Nash equilibrium predicts the outcome of this three-player game: both parties faithfully use...

Voting procedures are known to be plagued with a variety of difficulties such as strategic voting, or where a voter is rewarded with a better election outcome by not voting, or where a winning candidate can lose by receiving more support. Once we know that these problems can occur, the next...

A q-rule is where a winning coalition has q or more of the n voters. It is important to understand when, generically, core points exist; that is, when does the core exist in other than highly contrived settings? As known, the answer depends upon the dimension of issue space. McKelvey and...

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....

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...

A theory is developed to identify, characterize, and explain all possible positional and pairwise voting outcomes that can occur for any number of alternatives and any profile. This paper describes pairwise voting where new results include explanations for all paradoxes, cycles, conflict between...

A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be...