Fig. 5.

Recovering from polarization. We numerically calculated the size of the basin of attraction for the high-polarization state, which determines the escape frequency—that is, the proportion of the population that must simultaneously adopt a low-polarization behavior to escape the high-polarization equilibrium. We show the escape frequency as a function of the baseline environment, ${\theta }_0$, and the (fixed) degree of sorting, $\chi$. For intermediate values of theta, risk aversion means that it becomes increasingly difficult to reverse polarization (higher escape frequency, darker colors). However, when the environment is very bad, and risk tolerance dominates, or if the environment is very good, it becomes possible to reverse polarization through the coordinated behavior of small frequency of low-polarization individuals. When the environment is good and sorting is low, polarization is easiest to reverse without entering a highly deleterious environment. Other parameters are set to $B_I=1$, $B_O=2$, $q_I=1.0$, $q_O=0.6$ with $h=10$ and $a=0.02$, while $\gamma =0$, $\beta =0.5$, ${\theta }_0=0.5$, and $r=1$ unless otherwise stated.