Partial homogeneity structure and its impact on players’ power. Hybrid power indices

The paper presents the probabilistic interpretation of Shapley-Shubik index and Banzhaf value and the concept of partial homogeneity structure. Probabilities of being critical can be calculated based on this structure. These probabilities constitute the basis for calculating hybrid power indices, Shapley-Shubik index and Banzhaf index being the extreme cases. The paper presents the idea of reconstruction of partial homogeneity structure based on maximum likelihood estimation. This method is based on the same assumptions as hybrid power indices. The method is illustrated by simple heuristic examples and results of analysis of clubs’ voting in 7th term of Sejm – the lower house of the Polish parliament.