The paper uses an experimental approach to study the voting power distribution in the context of classical preferences, as well as in generalized form which takes into account players’ preferences to coalesce with each other. Our results extend those of Montero, Sefton & Zhang (2008), confirming their basic findings using independent experimental data, and explain some of their empirical paradoxes. A major result of our experiment is that even small modifications of preferences lead to statistically significant differences in players’ shares, justifying the use of generalized power indices over classical ones. Furthermore, we demonstrate that the interplay of preferences significantly affects the process of bargaining and the resulting coalitions.