The Certainty Bound: Structural Limits on Scientific Reliability

TL;DR

This paper reveals structural limits on scientific reliability imposed by binary significance-based publication systems, showing that even diligent researchers face inherent constraints on replicability and reliability.

Contribution

It introduces a formal framework analyzing how binary decision rules constrain scientific reliability and identifies mechanisms that can undermine replication success.

Findings

Replication rate estimated at 36% for psychology pre-reform.

Binary significance decisions contribute fixed information to posterior odds.

Framework connects statistical limits to philosophical theories of science.

Abstract

Explanations of the replication crisis often emphasize misconduct, questionable research practices, or incentive misalignment, implying that behavioral reform is sufficient. This paper argues that a substantial component is architectural: within binary significance-based publication systems, even perfectly diligent researchers face structural limits on the reliability they can deliver. The posterior log-odds of a finding equal prior log-odds plus log(Lambda), where Lambda = (1-beta)/alpha is the experimental leverage. Interpreted architecturally, this implies a hard constraint: once evidence is coarsened to a binary significance decision, the decision rule contributes exactly log(Lambda) to posterior log-odds. A target reliability tau is feasible iff pi >= pi_crit, and under fixed alpha this generally cannot be rescued by sample size alone. Two mechanisms can drive effective leverage to 1 without bad faith: persistent unmeasured confounding in observational studies and unbounded specification search under publication pressure. These results concern binary significance-based decision architectures and do not bound inference based on full likelihoods or richer continuous evidence summaries. Two collapse results formalize these mechanisms, while the Replication Pipeline Theorem and Minimum Pipeline Depth Corollary identify a quantitative evidentiary standard for escape. Using independently documented parameters for pre-reform psychology (pi about 0.10, power about 0.35), the framework implies a replication rate of 36%, consistent with the Open Science Collaboration. The framework also provides quantitative bridges to Popper, Kuhn, and Lakatos. In low-prior settings below the single-study feasibility threshold, the natural unit of evidence is the replication pipeline rather than the individual experiment.