The paper uses an experimental approach to study the voting power distribution. Using Montero, Sefton & Zhang (2008), we confirm their basic findings and explain some of their empirical paradoxes. Our main contribution deals with the question of how voters’ preferences to coalesce influence their behaviour and payoffs. We extend the basic design to allow for asymmetric voters' preferences depending on the coalitions they take part in. The results show that even small modifications of preferences lead to statistically significant differences in players' shares, justifying the use of generalized power indices over classical ones.