Abstract
This essay discusses the power of an m-member subgroup of an N-member (N = 2n + 1) voting body, whose members vote either ‘yes’ or ‘no’ to a given issue. Passage or defeat of an issue is determined by simple majority. The power of the subgroup is defined as the probability that the outcome of a vote changes if all the members of the group reverse their votes. We assume that across a sequence of issues voters' behavior can be described by a Pólya-Eggenberger probability model, containing a parameter interpretable as group cohesiveness. Special cases are bloc voting and completely independent voting. Our model allows us to study interesting intermediate cases, i.e., situations where group cohesiveness is less than that of bloc voting yet stronger than in the case of independence. Satisfaction, defined as the probability of voting with the majority, and individual power are discussed in the light of the model.
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