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The Rationality of Crowd Intelligence

This monograph develops a unified geometric theory of crowd intelligence, decision-making, and collective rationality grounded in reinforcement, memory, and interaction. Its primary theoretical point of departure is the ternary crowd intelligence information model introduced by Tang Chenyue et al. in Journal of Systems Engineering and Electronics, Vol. PP, No. 99 (January 2026),originally proposed for emergency risk assessment. That model integrates hardware perception, media perception, and expert (group) perception through cloud-model parameters—expectation, entropy, and hyper-entropy—capturing both uncertainty and uncertainty about uncertainty in complex socio-technical systems. Building on this foundation, the present work generalizes the ternary cloud model into a comprehensive framework of cognitive fields. At the micro level, it introduces S-theory, in which reinforcement and memory constitute the minimal mechanisms of information processing, and formalizes these dynamics through S urn models. At the macro level, it derives continuous limits leading to stochastic differential equations, diffusion processes, and information geometry. These developments culminate in the definition of signature space, parameterized by a phase coordinate, a curvature (susceptibility) coordinate and a memory coordinate.