A set of new power indices is introduced extending Banzhaf power index and allowing us to take into account agents’ preferences to coalesce. An axiomatic characterization of intensity functions representing a desire of agents to coalesce is given. A set of axioms for new power indices is presented and discussed. An example of use of these indices for Russian parliament is given.
Keywords: Power indices, Banzhaf index, coalition, preference, intensity function, axioms