The System Coherence Index (SCI): A Directional Shock-Response Measure of Alignment in Complex Social Systems

This paper introduces the System Coherence Index (SCI), a value-neutral, directional metric designed to quantify how complex social systems align under external stress or constraint. Rather than measuring outcomes as “good” or “bad,” the SCI captures whether multiple subsystems respond in the same directional sense—specifically, whether they move toward increased or decreased degrees of freedom when subjected to a shock. The SCI is formally defined as a normalized sum of directional indicators, where each indicator reflects whether a subsystem exhibits movement toward greater constraint (+1), greater freedom (−1), or no meaningful change (0). By construction, the index ranges from 0 (no coherent alignment) to 1 (full directional coherence), and is intentionally insensitive to magnitude, focusing instead on structural alignment. Three empirical case studies demonstrate the SCI across distinct domains and scales: U.S. Congressional polarization and party unity during periods of structural political stress, Texas economic stability and legislative disruption surrounding major economic shocks, and U.S. electric grid reliability during the COVID-19 period using national SAIDI and SAIFI metrics. To ensure reproducibility and methodological transparency, the paper includes: Explicit indicator definitions and direction rules, Step-by-step SCI calculations for each case study, Locked legacy datasets as originally analyzed, and A side-by-side appendix comparing legacy and revised public datasets, demonstrating the directional invariance of the SCI under data revisions. This release establishes Version 1.0 of the directional (sign-only) formulation of the System Coherence Index, intended as a general-purpose tool for analyzing shock-response alignment in complex systems. Future extensions may incorporate magnitude weighting, temporal decay, or application at larger (macrosocial) or smaller (individual and psychological) scales.