Measuring Voting Power in Complex Shareholding Structures: A Public Good Index Approach

We propose a new game-theoretical method to measure the indirect control power of firms as elements of a whole corporate network. Our method considers voting rights attached to individual firms and indirect ownership relations. Our method builds upon the Karos and Peters method introduced in 2015. More precisely, instead of the (Shapley and Shubik, American Political Science Review 48:787–792, 1954) index used in the Karos and Peters framework, we propose the Public Good Index (PGI) introduced by Holler in 1982. In this way, we obtain a method based on minimal winning coalitions allowing us to measure the control power of all firms involved in complex shareholding structures. We also try to discuss the appropriateness of using the Public Good Index critically. Moreover, this method is used to estimate the indirect control power in a theoretical example of a shareholding structure and compared with the Karos and Peters approach for measuring the control power of firms.