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.

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.