Measures of Powerlessness in Simple Games

Consider a simple game with n players. Let ψ_i be the Shapley–Shubik power index for player i. Then 1-ψ_i measures his powerlessness. We break down this powerlessness into two components – a `quixote index' Q <sub>i</sub> (which measures how much of a `quixote' i is), and a `follower index' F <sub>i</sub> (which measures how much of a `follower' he is). Formulae, properties, and axiomatizations for Q and F are given. Examples are also supplied. This revised version was published online in June 2006 with corrections to the Cover Date.