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This paper examines a recent debate in the literature on power indices in which classical measures such as the Banzhaf, Shapley-Shubik, and Public Good indices have been criticized on the grounds that they do not take into account player preferences. It has been argued that an index that is blind to preferences misses a vital component of power, namely strategic interaction. In this vein, there has been an attempt to develop so-called strategic power indices on the basis of non-cooperative game theory. We argue that the criticism is unfounded and that a preference-based power index is incompatible with the definition of power as a generic ability: ‘the ability to affect outcomes’. We claim that power resides in, and only in, a game form and not in a game itself.

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.

Johnston (1978), Deegan andPackel (1979), andHoller (1982) proposed three power indices for simple games: Johnston index, Deegan-Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.