  The Shapley-Shubik index was designed to evaluate the power distribution in
committee systems drawing binary decisions and is one of the most established
power indices. It was generalized to decisions with more than two levels of
approval in the input and output. In the limit we have a continuum of options.
For these games with interval decisions we prove an axiomatization of a power
measure and show that the Shapley-Shubik index for simple games, as well as for
$(j,k)$ simple games, occurs as a special discretization. This relation and the
closeness of the stated axiomatization to the classical case suggests to speak
of the Shapley-Shubik index for games with interval decisions, that can also be
generalized to a value.
