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A Method for Evaluating the Distribution of Power in a Committee System


  • Shapley, L. S.
  • Shubik, Martin


In the following paper we offer a method for the a priori evaluation of the division of power among the various bodies and members of a legislature or committee system. The method is based on a technique of the mathematical theory of games, applied to what are known there as “simple games†and “weighted majority games.†We apply it here to a number of illustrative cases, including the United States Congress, and discuss some of its formal properties.The designing of the size and type of a legislative body is a process that may continue for many years, with frequent revisions and modifications aimed at reflecting changes in the social structure of the country; we may cite the role of the House of Lords in England as an example. The effect of a revision usually cannot be gauged in advance except in the roughest terms; it can easily happen that the mathematical structure of a voting system conceals a bias in power distribution unsuspected and unintended by the authors of the revision. How, for example, is one to predict the degree of protection which a proposed system affords to minority interests? Can a consistent criterion for “fair representation†be found? It is difficult even to describe the net effect of a double representation system such as is found in the U. S. Congress (i.e., by states and by population), without attempting to deduce it a priori. The method of measuring “power†which we present in this paper is intended as a first step in the attack on these problems.

Suggested Citation

  • Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
  • Handle: RePEc:cup:apsrev:v:48:y:1954:i:03:p:787-792_00

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