Decision Volume: A Structural Model of Cognitive Dimensionality, Agency, and Collapse

Abstract

Decision Volume introduces a structural invariant of cognition that quantifies a system’s total actionable capacity for coherent decision-making. Defined as the multiplicative interaction of breadth (available alternatives), depth (temporal and implicational extension), and integration (coherence among alternatives), decision volume provides a geometric measure of agency: V = B · D · I. The framework unifies cognitive stability, collapse, recovery, identity continuity, and the phenomenology of choice under a single volumetric model. Collapse occurs when decision volume falls below a functional threshold, producing predictable signatures such as narrowed alternatives, shortened horizons, distorted implications, and fragmented identity. Recovery is the ordered re‑expansion of breadth, depth, and integration. The model offers a structural reinterpretation of psychiatric conditions—including depression, anxiety, ADHD, trauma, mania, and dissociation—as disorders of decision‑volume dynamics. It further extends to artificial systems, proposing decision volume as a foundational quantity for evaluating coherence, stability, and collapse in computational agents.