When Does Optimization Become Incoherent? Irreversibility, Non-Compensability, and Feasible Choice

Optimization is the central organizing principle of economic analysis. Individual choice, social evaluation, and policy design are routinely formulated as the maximization of an objective function over a feasible set. This paper identifies a class of environments in which optimization itself ceases to be a coherent principle of evaluation. We study decision problems in which the domain of admissible actions includes losses that are irreversible, non-substitutable, and non-compensable. We show that, under minimal regularity conditions, no refinement of the objective function--such as state dependence, option values, or intertemporal trade-offs--can generally sustain coherent maximization on an unrestricted feasible set. In such environments, optimization necessarily leads to inconsistency: actions generating non-compensable losses may be selected as optimal whenever short-run gains dominate, regardless of how the evaluation criterion is specified. The main result is an impossibility theorem establishing that coherence failure is structural and does not stem from informational limitations, computational constraints, or ethical disagreement. We then provide a necessity result showing that coherence can be restored if and only if the feasible set is restricted so as to exclude actions that generate non-compensable losses. On the resulting restricted domain, standard optimization methods apply without contradiction. The analysis reframes irreversibility as a problem of feasibility design rather than objective-function design. It clarifies the limits of optimization-based evaluation and characterizes the minimal conditions under which optimization remains a valid principle of choice. This paper also serves as a foundational contribution to a broader research agenda on the structural limits of evaluation. By isolating the conditions under which optimization-based evaluation becomes incoherent, the analysis provides a unifying framework for understanding feasibility-based constraints across diverse economic domains. The analysis is intended to serve as a conceptual reference point for further work on feasibility, irreversibility, and evaluation, rather than to exhaust their possible applications.