Fig. 2.

Tipping points in the level of party identity. Polarization is measured as partisan difference (A and C) and extremism (B and D). A and B show a higher critical value in the polarizing trajectory than in the recovery trajectory. This means that there would be little effect on partisan divisions (A) or extremism (B) should the strength of party identity drop below $C_P$, the critical value at which rising polarization suddenly explodes. $C_P$ drops sharply when the level of intolerance increases from $\alpha$ = 0.1 to $\alpha$ = 0.3 (C and D); i.e., party identity does not need to be strong in order to trigger a phase transition to high polarization. Moreover, the hysteresis trajectory becomes asymmetric, indicating bifurcation and the irreversibility of polarization, even if the strength of party identity were to drop to zero.