Power Measurement as Sensitivity Analysis

Abstract

This paper proposes a unified framework that integrates the traditional index-based approach and the competing non-cooperative approach to power analysis. It rests on a quantifiable notion of ex post power as the (counter-factual) sensitivity of the expected or observed outcome to individual players. Thus, it formalizes players’ marginal impact on outcomes in both cooperative and non-cooperative games, for both strategic interaction as well as purely random behavior. By taking expectations with respect to preferences, actions, and procedures, one obtains meaningful measures of ex ante power. Established power indices turn out to be special cases.

The Inter-Institutional Distribution of Power in EU Codecision

“…As regards methodology, we employ new tools that are able to capture strategic inter-institutional interaction, which is not true for classical power measures. The study is the first of its kind, applying the framework for power measurement of Napel and Widgrén (2004). The framework generalizes the measurement ideas underlying e. g. the Penrose-Banzhaf or Shapley-Shubik indices to non-cooperative models and preference-based strategic interaction.…”

The Impact of Council Voting Rules on EU Decision-Making

“…For this reason, Napel and Widgrén (2004) propose to extend the above analysis from the simple coalition framework of a priori power measurement and the very basic voting game to a more general framework. First, take a player's marginal contribution as the best available indicator of his potential or ability to make a difference, i. e. his a posteriori power.…”

“…In this unified approach, impact is relative to a what-if scenario or what Napel and Widgrén (2004) call the shadow outcome. The shadow outcome is the group's decision which would have resulted if the player whose power is under consideration had chosen differently than he a posteriori did, e. g. if he had stayed out of coalition S when he a posteriori belongs to it.…”

“…Here, the first attempt is Steunenberg, Schmidtchen, and Koboldt (1999) who define power as the expected utility (using spatial preferences) that an actor obtains in the procedure when preferences are randomised. A more recent attempt is based on the strategic measure of power (SMP) that was introduced in Napel and Widgrén (2004) and applied in inter-institutional analysis of EU codecision in Napel and Widgrén (2006). The latter is based on an equilibrium analysis of procedural spatial voting games.…”

“…In particular, if one evaluates the distribution of power between the decision-making bodies in the EU the analysis contains two phases, first, the equilibrium analysis using non-cooperative procedural spatial voting model and, second, a priori analysis by randomising preferences. The method that we apply is described in the following (see Napel and Widgrén (2004)). …”