The impossibility of a preference-based powerindex

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.