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.