The Extraction–Legitimacy Loop: A Source-Blind Model with Constrained Predation

This paper presents a minimal dynamic model of the feedback loop between fiscal extraction, legitimacy erosion, and coercion costs. The extractor is modelled as a myopic monopolistic predator facing a closed budget identity. Two independent environmental parameters govern the system: K, an extraction constraint that enters the model through compliance elasticity, coercion effectiveness, and coercion cost; and H, an institutional composition parameter that determines the aligned share of post-obligation residual expenditure. Both K and H are treated as source-blind, aggregating multiple carriers of their respective roles. Orthogonal fiscal shocks S are likewise source-blind. Legitimacy is expressed through a logistic state variable bounded to the open unit interval, with dynamics that distinguish covered orthogonal expenditure from shortfall erosion. The reduced system admits four regime types — good, coercive, bistable, and runaway — whose structure in parameter space is characterised numerically. The principal finding, demonstrated through phase diagrams in independent (K, H) and (K, S) projections across multiple shock levels, is that regime type is determined primarily by K and S; under the parameter ranges examined, H plays a secondary role, with boundaries in the (K, H) plane running nearly vertically. This finding is non-trivial precisely because K and H are independent by construction; dominance of K is an emergent property of the closed-budget feedback structure, not a constructive feature of the allocation rule. Extensive sensitivity analysis and a full computational appendix are provided.