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Mathematical analyses of the distribution within legislative bodies of formal, constitutional power to initiate or prevent action, and of the organization's power to act. Using some, but not all, of the Shapley-Shubik measure of power, all possible voting subsets are examined but each is counted only once, without regard to the order of voting. Expressions are given for the power of the United States to enact legislation and the contribution thereto of the veto override -- probably .066 of the total. Analysis of the United Nations Security Council structure shows that it was nearly immobilized originally, and that subsequent enlargement had the effect of decreasing its powers still more. The difficulty of restraining any public nuisance, such as water pollution or false alarms, reflects the lesser power of the collectivity to act. Coalitions within bodies can either increase or decrease the organization's power, according to whether their internal rules are more or less restrictive. This analysis of the power given by the rules does not provide a basis for predicting behavior, but is a useful input to such predictions.
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