An essential feature of our extended model is the variable H(t)H(t)H(t), representing the black horse potential---the latent probability that a new challenger or outsider figure rises when systemic instability creates political openings. Unlike trust (TTT), economic stress (EEE), or protest intensity (PPP), the black horse potential is not directly observable until crystallization occurs. Instead, it can be modeled as an emergent state variable driven by two forces: systemic instability and leadership weakness.
1. Governing mechanism
We extend the reduced system with a fourth equation:
H=PP+EELL(1T)HH,\dot H \;=\; \sigma_P \, P \;+\; \sigma_E \, E \;-\; \sigma_L \, L \,(1-T) \;-\; \gamma_H H,H=PP+EELL(1T)HH,
where:
P\sigma_PP weights protest intensity as a driver of alternative figure emergence;
E\sigma_EE links black horse probability to economic hardship;
L\sigma_LL measures legitimacy as a suppressor of outsider viability;
H\gamma_HH is a decay term reflecting natural dissipation of outsider momentum in stable contexts.
In this representation, HHH rises when protests intensify and the economy weakens, especially under low legitimacy. Conversely, high legitimacy dampens HHH, while stable conditions reduce it over time.
2. Simulation insights
Numerical simulations illustrate how H(t)H(t)H(t) behaves under different leadership profiles:
Soeharto. High legitimacy and repression kept HHH suppressed for decades. Only when E\mu_EE surged during the 1997--98 Asian Financial Crisis did HHH rise abruptly, enabling outsider figures to emerge (e.g., Reformasi leaders).
SBY. Sustained legitimacy and moderate narrative control kept HHH low, even amid shocks. Outsider momentum was weak, and no black horse displaced him.
Jokowi. Narrative saturation lowered protest intensity, but when legitimacy wavered, HHH rose intermittently---manifest in recurrent outsider challenges in elections, though none unseated him during stable phases.
Prabowo. Low legitimacy combined with fragile repression balance elevates baseline HHH. Simulations show that even moderate protests can sustain black horse potential, making the regime vulnerable to outsider competition (e.g., figures like Anies Baswedan or populist celebrities).
3. Interpretation
The emergence of a black horse is thus not random but structurally predictable: it occurs when systemic stress pushes the equilibrium past crit\mu_{\text{crit}}crit, creating a positive feedback loop in HHH. Leadership quality, particularly legitimacy, acts as the main suppressor. Therefore, our simulations suggest that outsider breakthroughs are most likely under regimes that combine low legitimacy with rising economic stress and poorly calibrated repression.
V. Case Study: Indonesia
