We define ternary voting games (TVGs), a generalization of simple voti
ng games (SVGs). In a play of an SVG each voter has just two options:
voting 'yes' or 'no'. In a TVG a third option is added: abstention. Ev
ery SVG can be regarded as a (somewhat degenerate) TVG; but the conver
se is false. We define appropriate generalizations of the Shapley-Shub
ik and Banzhaf indices for TVGs. We define also the responsiveness (or
degree of democratic participation) of a TVG and determine, for each
n, the most responsive TVGs with n voters. We show that these maximall
y responsive TVGs are more responsive than the corresponding SVGs.