The Cascade of Inattention: Observability and Responsibility in Vertical Hierarchies

A companion working paper—the Equilibrium Without Collusion model (hereafter ewc; SSRN working paper, 2026)—showed that recurring control deficiencies can be an equilibrium without collusion: when a core auditor’s observability of a specialist’s work is low, declining to understand that work is individually rational, and the deficiency persists with no party deviating and no side payment changing hands. That mechanism turned on a single primitive—accountability is allocated in proportion to what one is seen to be able to observe. This paper nests that primitive vertically and shows that the nesting generates two results the single dyad cannot. In a three-tier hierarchy—executive, manager, employee—each monitoring relationship is an instance of the companion paper’s dyad, and the middle player is Janus-faced: observed from above, observer from below. The first result is a cascade of inattention: because the manager’s incentive to watch the employee is gated by the executive’s watching of the manager, a withdrawal of attention at the top propagates downward—if the executive does not watch the manager, the manager does not watch the employee, and the employee does not work. The executive’s watching is precisely what rescues the manager from his own strategic inattention. The second is a two-faced penalty: a heavier penalty on the manager sharpens his discipline of the employee (a structural consequence of the companion paper’s attribution premise) while making him less visible to the executive (the companion paper’s penalty paradox)—the same comparative static pointing in opposite directions at the two tiers, the net effect set by how much the upward paradox is transmitted back down through the cascade. Both results are established as monotone directions on a code-faithful three-tier model and verified across a grid of detection-curvature and diffuse-penalty values; discontinuities, thresholds, and magnitudes are flagged as functional-form-dependent throughout. A closing section generali 1 zes the frame from a single line to a branching hierarchy, where the same mechanism produces two effects a line cannot: under a bi 2 nding apex attention budget, disciplined and collapsed divisions coexist within one firm—the firm breaking symmetry even between identical branches—while relativ 3 e cross-branch evaluation attenuates the coexistence 4 . The audit dyad of the compa 5 nion paper emerges as the special corner of a general frame in which a monitor has neither credit for nor produ 6 ction stake in the work below—which is why it is the configuration most exposed to the pathology.