Evaluation of Banzhaf index with restrictions on coalitions formation

The generating functions representative of the Banzhaf power index of the parties, or political groups of electoral bodies, is applied to the case where particular parties simultaneously (in pairs) cannot be part of any coalition. For such types of restrictions on coalition formation, the two-stage procedure for evaluating the Banzhaf index using generating functions is presented. Throughout the steps of the procedure the adjusted Banzhaf index generating function polynomial is transformed to the standard representation used for the calculation of this index. The presented approach is discussed and the procedure is illustrated by several examples.