Figure 1.

Extension of Granovetter’s (graphic) model with P potentially and A certainly acting individuals. (a) The original model that computes the number of acting individuals $R(t+1)$ from the cumulative distribution function of thresholds $F$. The purple line indicates a typical normal-like choice for this distribution. The 45°-line (green) intersects $F$ at the stable (black) and unstable (white) equilibrium points R*. As for many realistic choices of $F$, only R* = 0 and R* = N are stable. (b) Introducing A certainly and P potentially acting individuals, such that the $C=P-A$ contingent individuals have the same threshold distribution $F$ as the entire population $N$. Here, the equilibria move to the interval $R^{⁎}\in [A,P]$ and are not necessarily located at exactly $R^{⁎}=A$ and $R^{⁎}=P$. Hence, the $A$ certainly acting individuals trigger some contingent individuals to act, too. (c) Rescaling $R(t+1)$ to the unit interval shows that equilibria can be computed by shifting the diagonal line from crossing $(0,0)$ and $(N,N)$ (as in (a)) to crossing $(A,0)$ and $(P,1)$ and using the same threshold distribution F as in (a).