Resumen de Strategic Power Revisited
A lively debate about the adequate tool for measuring decision power in real-life institutions such as the European Union has been sparked by Garret and Tsebelis (1999, G&T). Their verdict that power indices exclude variables that ought to be in a political analysis (institutions and strategies) and include variables that ought to be left out (computational formulas and hidden assumptions) has motivated many authors to defend traditional power indices by clarifying the supposedly hidden assumptions underlying power formulas, and giving reasons for not taking institutions and strategies corresponding to explicit decision procedures and rational, preference-driven agents into account.
Earlier attempts to take players� preferences into power index calculations include the Shapley-Owen modification of the Shapley-Shubik index (Shapley 1977, Owen and Shapley 1989). It, however, still neglects the procedural aspects of decision making. So, motivated by the recent debate, Steunenberg, Schmidtchen, and Koboldt (1999, SS&K) have proposed a new strategic power index (StPI) which explicitly takes both decision procedures and players� preferences into account.
We disagree with G&T�s critique on many points and in particular see an important role for a priori power analysis that does not rely on detailed knowledge of preferences on this and that policy issue. But, like SS&K, we see a need to have adequate tools for measuring power if information on preferences and procedures is available. Unfortunately, SS&K�s measure is not the right answer. It can yield extremely counterintuitive indications in rather basic examples and, for instance, give a player negative power despite normalization.
The latter makes sense once the P for power in the StPI is replaced by an S for success. Namely, on closer inspection, SS&K�s StPI turns out to be a useful measure of average success, however not one of power.
We propose an alternative unified approach. It takes up G&K�s critique but still allows for �sometimes merely convenient, sometimes desirable� a priori power measurement. Our approach rests on a player�s marginal contribution or marginal impact on the collective decision taken a posteriori as the primitive of power, comparing an actual outcome with a shadow outcome which alternatively could have been brought about by the considered player. This generalizes the concept of swings or pivot positions from cooperative games to non-cooperative games, and yields a measure of a posteriori power which is suited to take decision procedures and preferences into account. Having defined a meaningful measure of a posteriori power, meaningful a priori measures can be constructed. A priori-ness of different degrees can be considered, concerning players� preference-based or unmotivated actions, decision procedures, or both.
By making corresponding distribution assumptions, one obtains traditional a priori power indices such as the Penrose index or Shapley-Shubik index as a special case. More generally, our measure defines power as a player�s expected marginal impact, where expectation is taken with respect to an appropriate probability measure on (power-relevant) states of the world. Applications of our measure to the European Union are then discussed.
