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The Bias Amplification Model

A Mathematical Framework for Quantifying Cognitive Distortion Under Conditions of Information Overload

The Bias Amplification Model — White Paper Cover
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SSRN Preprint · April 2026

The Bias Amplification Model

Ron Franklin  &  Timothy Lewis  ·  San Diego, California  ·  2026

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 rate 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

Read on SSRN → ↓ Download PDF
Cognitive Overload Dual-Process Theory Cognitive Bias Attention Economy Decision Quality Phi Index Information Processing Behavioral Economics

The Master Equation

Φ(Ω) = Φ₀ + f(Ω) · Ā

Aggregate Bias Index as a function of the Cognitive Overload Ratio — driven by a sigmoid amplification function centered at Ω = 1.0

What the paper covers

A formal contribution to cognitive science.

The BAM white paper provides the full mathematical development of the framework — equations, parameter justifications, falsifiability conditions, and an operationalization roadmap for empirical validation.

Ω
The Core Ratio

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.

Φ
Seven Bias Equations

Individual mathematical formulations for each of the seven amplified biases — Confirmation, Availability, Substitution, Recency, Anchoring, Representativeness, and Framing — with baseline and amplification parameters.

∂
Four Cognitive Zones

The four-zone framework (Logical, Transition, Heuristic, Critical) with Phi boundaries, behavioral signatures, and decision-quality implications for individuals and institutions.

⊕
Falsifiability & Validation

Explicit falsifiability conditions, a full operationalization table (Table 2), proposed experimental designs, and the conditions under which empirical work would confirm or disconfirm the model's predictions.

Also available

Explore the model interactively.

The BAM is live as a real-time interactive tool. Set your cognitive parameters, explore the four zones, and see how Phi responds — no account needed.

Open the Interactive Model →

Cite or collaborate.

The BAM is released as an open theoretical contribution. We welcome scholarly scrutiny, empirical collaboration, and citation.

Contact the Authors

Franklin, 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