Threshold operationalisation
Define PcP_c (crisis threshold) empirically (e.g., protest sized events frequency or normalized index > 0.4).
Define HcH_c via social-media thresholds (follower growth, mention velocity) calibrated to historical emergent leader episodes.
4. Sensitivity: how small changes move ensembles
Ensemble runs show high sensitivity to three levers:
a. Relief responsiveness (U\rho_U) --- increasing U\rho_U by 25--50% reduces escalation probability dramatically (order-of-magnitude in some priors).
b. Coercive reach (K\rho_{\mathcal{K}}) --- increasing K\rho_{\mathcal{K}} increases short-term suppression but nonlinearly raises medium-term escalation risk through trust erosion.
c. Noise amplitude (\sigma) --- a single large jump can flip most ensemble members into the escalation basin even with moderate policy response.
5. Example decision rule (for operational use)
A simple, implementable early-warning decision rule derived from ensemble diagnostics:
If within 7 days: autocorr(P) by > 15% and r^t>1.1\hat r_t > 1.1 and Pr(P>Pc within 30d)>30%\Pr(P>P_c\ \text{within 30d}) > 30\%, then declare high-risk and execute an emergency relief + transparency package within 72 hours and restrict coercive deployments to targeted units only.
This rule is transparent, testable with historical back-testing, and can be incorporated into a policy dashboard.
