In mathematics monotonicity is used to denote the nature of the
connection between variables. So, 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.