  In this letter we propose two general models for paradigm shift,
deterministic propagation model (DM) and stochastic propagation model (SM). By
defining the order parameter $m$ based on the diversity of ideas, $\Delta$, we
study when and how the transition occurs as a cost $C$ in DM or an innovation
probability $\alpha$ in SM increases. In addition, we also investigate how the
propagation processes affect on the transition nature. From the analytical
calculations and numerical simulations $m$ is shown to satisfy the scaling
relation $m=1-f(C/N)$ for DM with the number of agents $N$. In contrast, $m$ in
SM scales as $m=1-f(\alpha^a N)$.
