Catastrophic decisions

This monograph develops a geometric theory of decision, belief, and social dynamics in which preferences are no longer treated as smooth functions of probabilities but as equilibria on curved cognitive manifolds. Classical models of rational choice - Expected Utility, Rank-Dependent Utility, and Cumulative Prospect Theory - fail to account for systematic empirical anomalies such as Birnbaum-type paradoxes, preference reversals, hysteresis, and sudden belief collapse. We argue that these phenomena are not errors or biases, but structural consequences of curvature, inequality, and geometric instability