CFT implements five fundamentally different models of collective behavior within a unified comparison framework: Consensus-Fracture (threshold-based cliques), Gradient Field (continuous force-based clustering), Quantum Social (probabilistic superposition with observer effects), Information Cascade (entropy-driven formation), and Thermodynamic (statistical mechanics phase transitions). A prediction tournament scores each theory on accuracy, dynamic fidelity, parameter sensitivity, and cross-theory agreement against the same dataset. Designed to answer which mathematical assumptions are necessary vs. convenient for modeling coalition dynamics in political systems, online communities, and organizational structures.