Games with multiple alternatives enlarge the domain of social situations mo
delled by the classical cooperative game theory. In this paper, we prove th
at any linear value defined for traditional cooperative games admits a natu
ral extension to games with multiple alternatives. A method to compute the
extended values is also provided. As specific examples, we present an appli
cation of the Shapley value and the Banzhaf-Coleman index to two voting sit
uations taken from the real world.