A mathematical framework for quantifying cognitive distortion under conditions of information overload
The relationship between information load and cognitive bias has been theorized but not formally modeled. This paper introduces the Bias Amplification Model (BAM), a mathematical framework that quantifies how elevated information-processing demands systematically amplify seven well-documented cognitive biases. The model's core variable, the Cognitive Overload Ratio (Ω = I/C), expresses the ratio of information input to cognitive processing capacity. As Ω approaches and exceeds 1.0, a sigmoid amplification function drives nonlinear increases in seven bias intensities — aggregated into the Phi Index (Φ), a composite measure of overall cognitive distortion.
Publication Status
Now available on SSRN · April 2026 · ISBN 979-8-9992593-7-0
The Master Equation
Aggregate Bias Index as a function of the Cognitive Overload Ratio — driven by a sigmoid amplification function centered at Ω = 1.0.
The BAM white paper provides the full mathematical development of the framework — equations, parameter justifications, falsifiability conditions, and an operationalization roadmap for empirical validation. It also develops a composite account of cognitive capacity and a formal prescriptive layer.
Full derivation of the Cognitive Overload Ratio Ω = I ÷ C, its relationship to dual-process theory, and the sigmoid amplification function f(Ω) that connects information load to bias intensity.
Individual formulations for each amplified bias — Confirmation, Availability, Substitution, Recency, Anchoring, Representativeness, and Framing — with baseline and amplification parameters aggregated into the Phi Index.
The four-zone framework — Logical, Transition, Heuristic, Critical — with Phi boundaries, behavioral signatures, and decision-quality implications for individuals and institutions.
The model treats capacity C as a composite — biological, schema-augmented, and externalized — and introduces metacognitive monitoring (M). Together they yield five prescriptive intervention levers, mapped to Awareness → Friction → Reclamation.
Explicit falsifiability conditions, a full operationalization table, proposed experimental designs, and the staged calibration program under which empirical work would confirm or disconfirm the model's predictions.
The BAM is live as a real-time interactive tool. Set your cognitive parameters, explore the four zones, and watch how Phi responds — no account needed.
Open the interactive model →The BAM is released as an open theoretical contribution. We welcome scholarly scrutiny, empirical collaboration, and citation.
Contact the authorsFranklin, R., & Lewis, T. (2026). The Bias Amplification Model: A Mathematical Framework for Quantifying Cognitive Distortion Under Conditions of Information Overload. AttentionPlease®. ISBN 979-8-9992593-7-0.
Or write to us directly: research@attentionplease.ai