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Voting power and voting blocs

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We use the method of power indices to analyse voting power of members of a hypothetical legislature that has voting blocs. We assume social actors are motivated by the pursuit of constitutional power as measured by objective power indices, following Riker (Behavioural Science, 1959, “A test of the adequacy of the power index”) and Coleman (American Sociological Review, 1973, “Loss of Power”). We apply the Penrose index (the absolute Banzhaf index) to a voting body with 100 members. We show how the power indices of individual bloc members can be used to study the implications of the formation of blocs and how voting power varies as bloc size varies. We argue that the Shapley-Shubik index is inapplicable to this context and show that the Shapley-Shubik index per head – which has been used in some studies -is inappropriate. We briefly consider incentives to migrate between blocs. This technique of analysis has many real world applications to legislatures and international bodies. It can be generalised in a number of ways: our analysis is a priori, assuming formal voting and ignoring actual voting behaviour, but can be made empirical with voting data reflecting behaviour; the paper examines the consequences of two blocs but can easily be extended to more.

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