Is it Better to Be Powerful or Lucky?: Part I

Abstract

This paper is divided into two parts. Part I contains a critique of two existing ‘power indexes’—the Shapley-Shubik index and the Banzhaf index. Part II begins with a rigorous analysis of the relationship between luck, decisiveness and success. It is shown then that the supposed ‘paradoxes of power’ generated by the other indexes can be easily dissolved. An extended application of the method of analysis to the US Constitutional Convention of 1787 follows. Finally, the relation between decisiveness (a probability) and power (a capability) is presented, and the question posed in the title is answered. At two points, the relevance of the conceptual points made to the pluralist-elitist debate is made explicit, and support is offered for the view that each side's conclusions follow from its assumptions about the nature of power.