Measures of (a priori) power play a useful role in assessing the character of interpersonal interaction found in collective decision making bodies. We propose and axiomatically characterize an alternative power index to the familiar Shapley/Shubik and Banzhaf indices which can be used for such purposes. The index presented is shown to be unique for the class of simple n-person games. By subsequent generalization of the index and its axioms to the class of n-person games in characteristic function form we obtain an analog to the Shapley value.

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The College Mathematics Journal. Ed Packel (packel@lakeforest.edu) did his undergraduate work at Amherst College and received a Ph.D. in functional analysis from M.I.T. in 1967. Since 1971 he has taught at Lake Forest College, where he served as department chair from 1986 to 1996. His research interests have oscillated among functional analysis, game theory, social choice theory, information-based complexity, and the use of technology (Mathematica) in teaching. His recreational enthusiasms have somehow gravitated towards sports where low numbers are good-namely, competitive distance running and golf. David Yuen (yuen@lakeforest.edu) did his undergraduate work at the University of Chicago and received his Ph.D. from Princeton University in 1988. Since 1995 he has taught at Lake Forest College, where he is now department chair. His current mathematical research is in Siegel modular forms. He is co-author (with Craig Knuckles) of the book Web Applications, written as a result of his computer science interests. As a youngster, he was on the world-champion 1981 USA Math Olympiad Team.

It is well known that group decision processes (of which voting processes are an important special case) do not in general have equilibria. In fact, recent work indicates that such processes are characterized by a degree of instability much more extensive than previously recognized. As observers of ongoing political processes, we contend that such instability results simply do not describe real world politics. As an alternative, we propose a nonequilibrium model which assigns a probability distribution to the objects of political decision. Although this Markov model is based on several specific propositions about the process by which legislative bodies move from one position to another, our theoretical results do not depend on these specific propositions: Given alternative substantive assumptions, our model would produce different predictions about outcomes. This version of the model, however, successfully simulates the results of a series of experiments performed several years ago.