: 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.

The paper presents issues concerning oceanic games. The theorems, which have been discussed, make it possible to apply Shapley-Shubik index to games with infinite number of players. Social interpretations of the presentedmodel have also been shown. Determinants of bandwagon effect observed in social reality have been described in detail. Results of applying oceanic gamesmodel to the analysis of last pre-election competition between Barack Obamaand Hillary Clinton have been presented.