The Relationship Between Shareholding Concentration and Shareholder Voting Power in British Companies: A Study of the Application of Power Indices for Simple Games

This paper reports an analysis of the relationships between shareholding and voting power distributions in a sample of British companies. It applies two standard approaches to the measurement of power in simple games: the Shapley-Shubik and the Banzhaf power indices. The results indicate that power is more concentrated than ownership in every case. A comparison of the two indices reveals that typically the Banzhaf index gives a more concentrated power distribution. For the Shapley-Shubik index the power ratio for the largest shareholder is accurately described in terms of the size of holding and the concentration of the remainder. The corresponding Banzhaf power ratio is less dependent on these variables. There is no association between power concentration and company size.