  R. Rim\'anyi defined the incidence class of two singularities X and Y as
$[X]|_Y$, the restriction of the Thom polynomial of X to Y. He conjectured that
(under mild conditions) the incidence is not zero if and only if Y is in the
closure of X. Generalizing this notion we define the incidence class of two
orbits X and Y of a representation. We give a sufficient condition (positivity)
for Y to have the property that the incidence class $[X]|_Y$ is not zero if and
only if Y is in the closure of X for any other orbit X. We show that for many
interesting cases, e.g. the quiver representations of Dynkin type positivity
holds for all orbits. In other words in these cases the incidence classes
completely determine the hierarchy of the orbits. We also study the case of
singularities where positivity doesn't hold for all orbits.
