Exact Finite-Size Scaling Theory Reveals Hybrid Transitions in Granovetter Threshold Cascades
Fontanari provides the first exact finite-N scaling theory for Granovetter-style social tipping, identifying hybrid transitions and precise power-law scalings of the critical window. The work bridges analytic theory with observable cascade statistics in finite populations. It supplies falsifiable predictions for how population size governs the sharpness and predictability of collective mobilization.
Next steps include embedding the exact scaling relations into agent-based models of real mobilization platforms to test whether observed cascade sizes follow the predicted N^{-1/3} or N^{-1/4} windows. Empirical datasets from petition platforms or protest recruitment could falsify the Beta-distribution assumption or reveal additional heterogeneity effects. The theory also supplies a quantitative benchmark for interventions that aim to shift the location of the critical endpoint through changes in threshold distributions.
Fontanari: Large-scale mobilization datasets from 2027-2028 will confirm the predicted N^{-1/3} critical-window scaling for power-law-like thresholds within measurement error.
Sources (3)
- [1]Primary Source(https://arxiv.org/abs/2608.20555)
- [2]Granovetter Threshold Model(https://www.jstor.org/stable/2778111)
- [3]Centola Complex Contagions(https://www.science.org/doi/10.1126/science.1157057)