The Theory of Residual Free Will (Observable Indeterminacy): Choice as a Deterministic Remainder

Economic agents often appear to exercise choice, even though their actions may arise from entirely deterministic processes. When individuals observe only low-dimensional projections of their own high-dimensional internal states, such as evolving preferences or neural configurations, their behaviour exhibits Residual Free Will, which is a structured set of apparently feasible actions shaped by unobserved variation. The paper formalises this idea through Observable Indeterminacy, which characterises when and how deterministic systems generate the appearance of stochastic choice due to informational constraints. This framework provides deterministic microfoundations for random utility models and reinterprets econometric error terms as projections of hidden but lawful dynamics. It yields empirical predictions that distinguish residual-based randomness from true noise, i.e., choices lie on lower-dimensional manifolds, individual deviations are temporally persistent, and violations of revealed preference arise from unobserved preference evolution rather than irrationality. Applications to consumer theory, market equilibrium, and welfare analysis demonstrate how core economic patterns emerge without assuming fundamental uncertainty. By grounding stochastic behaviour in the geometry of partial observability, the theory reconciles determinism with meaningful choice and reorients the interpretation of randomness in economic data.