Strategic Power Index

Limitations

The use of these indices has several limitations. First, the Shapley—Shubik Index assumes that all winning coalitions have the same value or total payoff, which is a basic assumption of the underlying theory of simple games. This constant-sum assumption is not very helpful for analyses of different institutional arrangements, because whatever some players gain others must lose. Second, both measures use only the voting rule in structuring decision making, ignoring other important rules concerning the type of proposals or amendments that can be made and the structure of the agenda for voting on them. Finally, by using permutations, the indices do not capture the possible impact of strategic considerations that players may have in a noncooperative game.

Alternative Approaches

For these reasons an alternative approach has been developed, producing a strategic power index. Bernard Steunenberg, Dieter Schmidtchen, and Christian Koboldt first proposed to combine noncooperative modeling of decision making with a measure of a player's power. Their approach included four distinct elements: (1) the modeling of a decision-making situation using the tools of noncooperative game theory, (2) the definition of a space of preference profiles together with status quo points, (3) a distribution of these profiles including status quo points (i.e., state variables), and (4) the use of an index to measure power based on different states of the world.

The first step of this approach is to formulate a game-theoretical model of a policy-making process. Such a policy game consists of all usual elements, including a specification of the players, their preferences, the current state of affairs or status quo, players' action sets, a possible sequence of moves, the distribution of information among players, and so on. The structural elements of a game constitute what is called a game form, that is, the elements without player preferences and status quo points. In principle, a game form determines who is permitted or required to do what and when in some decision-making situation. A game form may function, at least in the short term, like a riverbed through which motivations flow toward outcomes. Playing a game with the same game form but different motivations may lead to different outcomes. If players have Euclidean preferences, as is assumed, the distances to these outcomes can be regarded as an expression of a player's success in playing this game.

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