We investigate the applicability of voting power indices, in particular the Penrose index (aka absolute Banzhaf index), in the analysis of voting blocs by means of a hypothetical voting body. We use the power of individual bloc members to study the implications of the formation of blocs and how voting power varies as bloc size varies. This technique of analysis has many real world applications to legislatures and international bodies. It can be generalised in many ways: the analysis is a priori (assuming formal voting and ignoring actual voting behaviour) but can be made empirical with voting data; it examines the consequences of two blocs but can easily be extended to more.