: The paper presents the probabilistic interpretation of ShapleyShubik 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, ShapleyShubik 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.

This paper aims to present a theoretical concept that allows to investigate decision-making in large and ideologically differentiated bodies. Former models of oceanic games were based on the assumption of equal disposition to cooperate with other players among all voters. It is impossible to hold this assumption in a political reality. The paper develops the concept of "hybrid power indices" for oceanic games. Oceanic games with a partial homogeneity structure are analysed in the paper. The paper is the result of my previous studies of decision-making processes in large assemblies and my efforts in modelling ideological differentiation in political bodies. The paper also shows that presented formal models have solid foundations in classical sociological theories.
The last part presents several convenient and reliable sociological interpretations of the models as well as my plans for future studies using the models described.

Unlike the classical approach to voting power, the approach presented in this paper makes a distinction between a voter's winning and blocking power and relates the latter kind of power to the number of small-size minimal blocking coalitions the voter can form with other voters. It is shown that the concept of blocking sheds light on the designing of voting systems for EU Council of Ministers from the very beginning to the Lisbon treaty.