A power index in a simple game with multialternatives

We consider a simple game with multialternatives, in which each player votes only one alternative and a winning alternative is only one. Since more than two coalitions may be formed simultaneously, its characteristic function must be defined on not only a coalition but also a division of the set of voters. We propose a new power index denoting the influence of each player upon a collective decision making and show an axioms system on which it is based.