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In this paper we argue that spatial voting games and power index models are not necessarily exclusive ways to analyse EU decision-making. We find that the two main criticisms pointed out by scholars of spatial voting games, namely that power indices do not take into account preferences or the role of the agenda-setter, are not fully valid as spatial voting games deal with complete whereas power indices deal with incomplete contracts. Ideas for combining the two so far very opposite views are then discussed.

The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. The book revisits the themes discussed in the well-known 1982 publication "Power, Voting and Voting Power" (edited by Manfred J. Holler). Thirty years later this essential topic has been taken up again and many of the authors from its predecessor participate here again in discussing the state-of-the-art, demonstrating the achievements of three decades of intensive research, and pointing the way to key issues for future work

In recent years, publications on power indices and coalition formation have multiplied. Obviously, the application of these concepts to political institutions, more specifically, to the analysis of the European Union and, as it seems, the election of the President of the United States is getting more and more popular. There are, however, also new theoretical instruments and perspectives that support these applications: First of all, the probabilistic model of coalition formation has to be mentioned which is made operational by the multilinear extension of the characteristic function form of coalition games. This instrument triggered off a reinterpretation of existing power indices and the formulation of new indices. This development is accompanied by an intensive discussion of the concept of power in general - what do we measure when we apply power measures? - and the properties that an adequate measure of power has to satisfy. Various concepts of monotonicity were proposed as litmus test. The discussion shows that the underlying theories of coalition formation play a decisive role. New results will be discussed in this volume. Its contributions put flesh and blood on the theoretical innovations and their applications that led to a growing interest in power indices and coalition formation