The Performance of Shareholder Influence Measures: An Empirical Assessment of Share in Votes, Banzhaf Index, and Shapley-Shubik Index

Abstract

The ownership structure is one of the central fields in corporate governance research. Ownership structure metrics provides several measures of shareholder influence. However, there is little empirical evidence to assess the absolute and relative performance of these measures. This gap in the literature is mainly caused by the difficulty to establish an adequate test procedure. This research contributes to filling the gap in the literature by suggesting a new test approach. The power of a shareholder should be reflected in his representation in the board. The ability of the influence measures to explain board representation can be applied to evaluate absolute and relative performance of the influence measures. The measures of shareholder influence comprise the share in voting rights, the Shapley-Shubik index, and the Banzhaf index, from all of these measures several variants enter the analyses. For a sample of German corporations, the basic finding is that the simple share in votes is able to fend off all competitors in the capability to explain principal shareholder supervisory board representation. In addition it can be noted that, in a general perspective, the many variants of both power indices with consideration of unknown votes make up a rather homogenous group. Consequently, it does not matter much which of the variants is chosen. Both power variants with adjusted majority requirement make up a distinct group of measures, which usually perform worst.