Computational Complexity of Organizational Decision Hierarchies

We model organizational decision hierarchies as bounded-span monotone threshold circuits, capturing tradeoffs between decision latency, accuracy, and headcount. Aggregating n binary signals with span s requires depth at least ⌈logs n⌉;we formalize OrgTree-Design and evaluate a simple greedy heuristic. Full complexity analysis is out of scope. Simulations with n = 256, spans s ∈ {4, 8, 16}, and noise p ∈ {0.01, 0.05, 0.10, 0.20} show wider spans reduce latency butlower accuracy (e.g., at p = 0.10, s = 4 to s = 16 cuts latency from 3.6 to1.8 time units but drops accuracy from 100% to 89.7% (95% CI [82.1, 90.7])). Welch ANOVA on p = 0.10 data confirms span effects (F (2, 997.2) = 687.58,p < .001, ˆϵ2 = 0.479). Medium spans (s = 8) offer a balanced Pareto point for hybrid organizations Jacobsen (2023). Our framework links span-of-control theory to circuit complexity, providing a reproducible basis for hierarchy design.