Part VI - COLLAPSE: a quantitative method for detecting systemic bias

This paper introduces Collapse analysis: a quantitative statistical framework for determining when a pattern of uniformly adverse outcomes across multiple domains becomes incompatible with ordinary stochastic fluctuation.

The method formalises a conservative null hypothesis of benign variation and evaluates whether an observed directional configuration can plausibly arise under independence, copula-based dependence, exchangeable models, or bounded correlation. Across all admissible stochastic regimes, the probability of full directional alignment decays exponentially in the number of affected domains. When this probability falls beneath actuarial materiality, continued reliance on the innocent hypothesis becomes statistically and decision-theoretically irrational.

The framework integrates:

• binary domain modelling,

• correlation stress-testing via Gaussian copulas,

• distribution-free bounded dependence,

• exchangeable de Finetti mixtures,

• Bayes factor divergence,

• and formal decision-theoretic dominance thresholds.

Unlike traditional comparator-based or narrative approaches, the test operates solely on the internal geometry of the outcome vector itself. It requires no motive attribution, no external benchmarks, and no subjective credibility reconstruction. When collapse is detected, the inference is evidential rather than causal: stochastic innocence ceases to be a coherent probabilistic hypothesis.

A fully synthetic case study demonstrates the method in practice. A non-technical appendix provides a practitioner guide for legal, regulatory, and governance users.

This paper contributes a formally defined, reproducible statistical instrument for identifying evidential implausibility as a diagnostic threshold for directional system behaviour. It is suitable for application in forensic statistics, regulatory audit, organisational governance, and algorithmic accountability.

Keywords: systemic bias; directional collapse; evidential statistics; multi-domain analysis; forensic probability; Bayesian convergence; governance diagnostics; actuarial modelling; dependency stress testing; stochastic innocence; statistical implausibility; algorithmic accountability; regulatory audit; organisational bias detection; decision-theoretic inference; high-dimensional tail risk.