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.