  We study the stabilization time of a wide class of processes on graphs, in
which each node can only switch its state if it is motivated to do so by at
least a $\frac{1+\lambda}{2}$ fraction of its neighbors, for some $0 < \lambda
< 1$. Two examples of such processes are well-studied dynamically changing
colorings in graphs: in majority processes, nodes switch to the most frequent
color in their neighborhood, while in minority processes, nodes switch to the
least frequent color in their neighborhood. We describe a non-elementary
function $f(\lambda)$, and we show that in the sequential model, the worst-case
stabilization time of these processes can completely be characterized by
$f(\lambda)$. More precisely, we prove that for any $\epsilon>0$,
$O(n^{1+f(\lambda)+\epsilon})$ is an upper bound on the stabilization time of
any proportional majority/minority process, and we also show that there are
graph constructions where stabilization indeed takes
$\Omega(n^{1+f(\lambda)-\epsilon})$ steps.
