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May’s Theorem characterizes simple majority rule with the conditions of anonymity, neutrality, and positive responsiveness. We characterize the class of rules satisfying anonymity and positive responsiveness using the concept of a strong quota pair system. [ABSTRACT FROM AUTHOR]

In 1992, Klamkin and Liu proved a very general result in the Extended Euclidean Plane that contains the theorems of Ceva and Menelaus as special cases. In this article, we extend the Klamkin and Liu result to projective planes PG(2, ) where  is a field. [ABSTRACT FROM AUTHOR]

Abstract: Sen’s theorem, which highlights the conflict between the Pareto condition and individual rights, is a fundamental result in the area of social choice. In this paper, we give an analog of Sen’s theorem for consensus functions on hierarchies by showing that in almost all cases it is not possible to find a ternary Pareto consensus function where two distinct algorithms will have the same decisive impact on the consensus output. [Copyright &y& Elsevier]

The center function is defined on a connected graph G , where the input is any finite sequence of vertices of G and the output is the set of all vertices that minimize the maximum distance to the entries of the input. If the input is a sequence containing each vertex of G once, then the output is just the classical center of G . In the axiomatic approach, one wants to establish a set of properties or consensus axioms that characterize the function. We refer to an axiom as a universal axiom if the center function satisfies this axiom on any connected graph. In a previous paper, our focus was on classes of graphs on which we were able to characterize the center function in terms of universal axioms. In this paper, the focus is on classes of graphs on which these universal axioms do not characterize the center function. We introduce non-universal axioms that, together with some universal axioms, provide new characterizations of the center function: on cocktail party graphs, on complete bipartite graphs, and on block graphs. [ABSTRACT FROM AUTHOR]

Abstract: Consensus trees have been used routinely in systematic biology for over 30 years with the majority-rule consensus tree among the most popular. In this paper we give axioms that characterize a new consensus function, called majority-rule (+), that is based on a generalization of majority-rule to the supertree case. In addition, two other related consensus functions are characterized. [Copyright &y& Elsevier]