Beyond Consistent Scenarios: Deriving Indirect Influence, Transition Resistance, and Adjustment Dynamics

Assessments of structural change and economic transition dynamics, such as those arising in the energy transition, depend on internally consistent qualitative scenarios specifying the policy environment, technology mix, governance arrangements, and demand conditions.

Cross-Impact Balance (CIB) analysis derives such socio-technical scenarios as fixed-point attractors of an expert-elicited interdependency network, supplying structural inputs upon which assessment models (including energy system optimisation, agent-based, and general equilibrium frameworks) can draw.

Standard CIB, however, delivers only this equilibrium catalogue, leaving four structural questions unanswered: how much network-weighted effort a given transition requires; which components are the true system-wide levers once indirect influence chains are counted; in what sequence the system adjusts; and how the network at a given attractor responds to an external shock.

This paper extends CIB through Linear Response Theory, exploiting a structural isomorphism between the CIB drift matrix and the Leontief input-output technology matrix.

Four analytical objects are derived in closed form: the Type I cross-impact multiplier, which aggregates all direct and indirect influence chains; the perturbation budget, a network-weighted and directionally asymmetric measure of transition effort; the impulse response function, which traces descriptor adjustment sequences and feedback-induced overshoots; and the unit-impulse shock profile, which characterises attractor-specific network sensitivity and yields a direct measure of structural resilience and susceptibility.

The framework is applied empirically to an energy-transition cross-impact matrix, yielding all four objects for five structural equilibria, and transfers to any domain in which pairwise influence scores encode structural interdependencies.