In this chapter we explain the concept of a priori voting power and how it is measured. The situation we address is that in which a decision-making body – such as a committee or legislature – makes its decisions by vote, subject to a given decision rule. We shall refer to the decision-making body as the assembly, and to each of its members as a voter. We shall usually denote the assembly by N and the number of voters by n. By a coalition we mean any set of voters: part of the assembly or its entirety. We confine ourselves to the simplest kind of decision rule: each voter must vote either for or against a proposed bill (that is, no abstentions); and the outcome must be either approval or rejection of the bill (that is, no ties). The decision rule specifies which divisions of the assembly into ‘yes’ and ‘no’ voters result in approval of the proposed bill, and which in its rejection. By the a priori voting power of a given voter under a given decision rule we mean, roughly speaking, the extent of potential ability to affect the outcomes of divisions that this voter possesses by virtue of the decision rule alone. This italicized qualification is of crucial importance: it distinguishes a priori from actual or a posteriori voting power. We shall return to this in section 8.5.
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