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 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...

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 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....

This article characterizes all of the continuous social welfare orderings which satisfy the Weak (resp. Strong) Pareto principle when utilities are ratio-scale measurable. With Weak Pareto, on both the nonnegative and positive orthants the social welfare ordering must be representable by a...

The requirement that a voting procedure be immune to the strategic withdrawal of a candidate for election can be formalized in different ways. Dutta, Jackson, and Le Breton (Econometrica, 2001) have recently shown that two formalizations of this candidate stability property are incompatible with...