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On types of responsiveness in the theory of voting

Holler M. J., Nurmi H.

Operations Research and Decisions

2016

Vol. 26, No. 2

87--106

In mathematics, monotonicity is used to denote the nature of the connection between variables. Hence for example, a variable is said to be a monotonically increasing function of another variable if an increase in the value of the latter is always associated with an increase in the other variable. In the theory of voting and the measurement of a priori voting power one encounters, not one, but several concepts that are closely related to the mathematical notion of monotonicity. We deal with such notions focusing particularly on their role in capturing key aspects of plausible opinion aggregation. Further, we outline approaches to analyzing the relationship of opinion aggregation and voting power and thereby contribute to our understanding of major components that determine the outcome of voting.

Two variations of the Public Good Index for games with a priori unions

Alonso-Meijide J. M., Casas-Mendez B., Fiestras-Janeiro G., Holler M. J.

Control and Cybernetics

2010

Vol. 39, no 3

839-855

This paper introduces two variations of the Public Good Index (Holler, 1982) for games with a priori unions. The first one stresses the public good property which suggests that all members of a winning coalition derive equal power. The second variation follows earlier work on the integration of a priori unions (Owen, 1977 and 1982) and refers to essential subsets of an a priori union when allocating power shares. Axiomatic characterizations of both indices are discussed. Numerical examples, one of them taken from a political setting, illustrate the new power indices presented in this paper.