This work presents the results of the first experiment in Russia on voting and voting power. The general formulation of this task goes back to the theoretical works on voting power measurement, which are based on the number of participants' votes and the configurations of the winning coalitions. We compare the explanatory power of the classical indices of that kind with that of a generalized power index introduced by one of the authors in 2006, which takes into account not only the number of votes, but also preferences of the participants towards coalescing with each other. Our results demonstrate that generalized power indices are more adequate then the classical ones from a descriptive perspective, and that this notion should apparently include many of those decision factors that were considered insignificant in the classic literature, but are of great practical importance.