collapse: a quantitative test for systemic bias

abstract

this paper introduces a quantitative method for detecting systemic bias through the structured assessment of statistically implausible multi-domain outcome patterns. the approach formalises collapse analysis, a reproducible statistical instrument with layered operational depth: a first-stage independence check requiring only domain classification and counting; a second-stage Monte Carlo dependency model for intermediate correlation stress-testing; and a final Bayesian update that formalises posterior convergence under conservative assumptions. where the probability of the observed configuration under the innocent model falls below actuarial materiality, the method treats the event as a quantitative evidentiary signal of systemic bias. the framework is implemented via a five-stage protocol: domain extraction, temporal clustering, conservative stochastic modelling, correlation stress-testing, and calculation of an irreconcilability threshold. The analysis explicitly distinguishes directional coherence from random variation and formalises the evidential significance of uniform multi-domain deviation following a triggering perturbation. statistical collapse is not presented as proof of motive; it is the quantitative rejection of the hypothesis that the observed pattern could reasonably emerge by chance. a fully synthetic case study demonstrates the method in practice, showing that a fifteen-domain adverse pattern emerging immediately after a triggering perturbation is actuarially incompatible with any plausible model of benign system behaviour. the resulting probability collapse provides a replicable foundation for evidential inference in legal, regulatory, and governance contexts. the paper therefore contributes a generalisable statistical test for systemic bias: transparent by design, computationally lightweight at entry, and progressively rigorous across modelling layers. unlike existing approaches — typically reliant on narrative reconstruction or comparator analysis — collapse analysis offers a formally quantifiable criterion for when an innocent organisational explanation becomes probabilistically untenable. the method requires no narrative reconstruction, no subjective interpretation, and no external corroboration beyond the outcome vector itself. it operates entirely on probabilistic structure under explicitly stated assumptions and remains formally neutral with respect to motive.

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