Description
This monograph develops a unified geometric theory of decision making under risk anduncertainty, grounded in the concept of cognitive fields. Departing from traditional curve-basedmodels - such as Expected Utility, Rank-Dependent Utility, and Cumulative Prospect Theory - itargues that many persistent anomalies in choice behavior arise not from irrationality or noise, butfrom a mismatch between classical axioms and the geometry of the cognitive space in which decisions unfold. The core formal construct is the Probabilistic Tension Kernel (PTK), a local kernel parameterized bya signature that generates cognitive potential, forces, curvature, and decision dynamics. When probabilities are embedded in such fields, preferences emerge as trajectories governed by stability, noise, and configuration, rather than as static evaluations. Classical rationality is recoveredas a special, low-curvature limit of this framework. Within this geometric perspective, systematic phenomena such as preference reversals, framinge ffects, order effects, and violations of coalescing invariance are shown to be phase-dependentfield effects. In particular, the preference paradoxes documented by Michael H. Birnbaum are reinterpreted as consequences of unstable or negatively curved cognitive fields, rather than as contradictions of rational choice. It is formally demonstrated that no version of Cumulative Prospect Theory can reproduce these effects in principle, due to its reliance on global probability weightingfunctions. The theory integrates deterministic and stochastic dynamics, information geometry, and phasetransitions, and clarifies the relationship between cognitive fields and quantum cognition:quantum-like contextuality and non-commutativity emerge as effective descriptions of locallylinearized, metastable regimes within curved decision spaces. Methods are provided for empirically reconstructing cognitive fields from behavioral data, diagnosing Birnbaum-type regimes, anddistinguishing structural instability from random error. Extending beyond individual choice, the framework is applied to economic, social, and ideologicalphenomena, including market volatility, bubbles, polarization, and narrative dynamics, allinterpreted as interactions of coupled cognitive fields. The monograph concludes by proposing Configural Rationality as a new normative concept: rationality understood as coherence with the local geometry and dynamics of the cognitive field, rather than adherence to global invariance axioms. In this view, decision making is not optimizationon a fixed landscape, but navigation in a curved and context-sensitive space.