It is well-known that formulas for decomposing the restriction of a representation of a finite group to a subgroup involve sums over conjugacy classes. We present here a generalization of these formulas to a particular class of continuous groups (real semisimple Lie groups), where sums over conjugacy classes are replaced by computations in equivariant intersection cohomology. As a consequence, we recover most of a well-known multiplicity one theorem for discrete series in the space of $L^2$ functions on a semisimple symmetric space, although our theorem also has multiplicity one implications for certain representations in the space of smooth functions on a semisimple symmmetric space. This talk is based on joint work with Ian Grojnowski.