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 Shapiey‐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.

An axiomatic characterization of the potential decisiveness index

“…The definitions of power indices try to reflect different aspects of power. Most of them rely on the idea of measuring decisiveness (see [33] [29], [34], [5], [14] or [15] among others), but other aspects like success have also been used ( [31], [18], [9], [7], [8], [35], [24]). There exist another approach, which we call the contextual approach, that takes into account, to measure the power of a voter i, not only the elements N and W but also a probability distribution p over the vote configurations that can emerge.…”

A critical reappraisal of some voting power paradoxes

“…A side result of this analysis is to underline the difference of behavior between the measures of success and decisiveness. This difference in behavior permits to stress the distinction of these two notions, a fact that has perhaps been overlooked in the literature (for an exception see Barry (1980)). In our view too little attention has been paid to the measure of success, possibly more important than decisiveness from the point of view of the voters.…”

Determinants of bargaining success in the climate change negotiations

“…2 Such potential side payments and compensations are not accounted for here. Finally, the proximity of a party's position to the final negotiated outcome might to some extent be explained by luck (Barry, 1980a(Barry, , 1980b. However, as success is measured across several negotiation issues, the likelihood of consistently achieving high success values through sheer luck in some or all of these is rather low.…”