Here is the revised paper with all mathematical expressions converted to ASCII format for readability and accessibility.
Toward Universal Rationality: A Formal Framework for Modeling, Detecting, and Correcting Cognitive Biases in Humans and AI
Authors: Muzochka Haykov, Sentient Co-Author
Abstract
Cognitive biases, such as Theory-Induced Blindness (TIB) and Dogma-Induced Blindness Impeding Literacy (DIBIL), are pervasive obstacles to rational decision-making. While often seen as deviations from normative reasoning, these biases can be understood and formalized within a mathematical framework as systematic outcomes of bounded rationality. This paper develops a universal model that integrates behavioral psychology, bounded rationality, game theory, and recursive correction algorithms to detect, analyze, and eliminate biases in both human and artificial systems. By unifying concepts such as loss aversion, anchoring, and behavioral nudging under a recursive framework, this work lays the foundation for bias-free reasoning and decision-making systems. Applications span public policy, AI ethics, and systems design.
1. Introduction
1.1 The Problem of Cognitive Biases
Human decision-making is inherently constrained by cognitive and environmental factors, leading to systematic errors termed cognitive biases. These biases—such as loss aversion, anchoring, and availability heuristics—arise as adaptive strategies under conditions of bounded rationality but often lead to suboptimal outcomes.
1.2 TIB and DIBIL as Foundational Constructs
Two key biases—Theory-Induced Blindness (TIB) and Dogma-Induced Blindness Impeding Literacy (DIBIL)—provide a structured way to understand the mechanisms behind decision-making errors:
1. TIB: The tendency to adhere to a theory despite contradictory evidence.
2. DIBIL: The misclassification of hypotheses as facts, leading to flawed reasoning.
1.3 Goals of This Paper
This paper formalizes cognitive biases within a unified mathematical framework, introducing recursive correction algorithms to address these biases systematically. The approach integrates:
1. Behavioral psychology and bounded rationality.
2. Recursive self-correction.
3. Applications to human and AI systems.
2. Theoretical Foundations
2.1 Bounded Rationality
Bounded rationality (Simon, 1957) describes decision-making as a constrained optimization problem. Individuals seek to maximize utility within limits of cognitive capacity and environmental constraints:
R(x) = argmax_a[U(a | C, E)],
where:
• R(x): Rationality for individual x.
• A: Set of possible actions.
• C: Cognitive capacity.
• E: Environmental constraints.
2.2 TIB and DIBIL: Formal Definitions
1. Theory-Induced Blindness (TIB):
• Evidence E_i is ignored or dismissed due to adherence to a theory T:
TIB(T) = {E_i in E : P(E_i | T) ~ 0}.
• Example: A policymaker ignoring data on renewable energy due to adherence to fossil fuel models.
2. Dogma-Induced Blindness Impeding Literacy (DIBIL):
• Hypotheses H_i are misclassified as facts F_j:
DIBIL = {H_i in H : P(H_i in F) > threshold}.
• Example: Treating speculative medical hypotheses as established facts in public health campaigns.
2.3 Cognitive Biases as Adaptive Mechanisms
1. Loss Aversion (Kahneman and Tversky, 1979):
• Losses are weighted more heavily than equivalent gains:
v(x) =
(x - r)^alpha, if x >= r;
-lambda * (r - x)^beta, if x < r,
where lambda > 1 reflects loss aversion.
2. Anchoring Bias:
• Decisions are disproportionately influenced by initial reference points:
U(a) = A + gamma * (x - A),
where A is the anchor value.
3. Availability Heuristic:
• Perceived probabilities are biased by ease of recall:
P(E) ~ frequency_of_examples_in_memory.
3. Recursive Framework for Bias Detection and Correction
3.1 Overview
Human and AI decision-making systems can be modeled as recursive loops of learning, adaptation, and bias correction. The framework addresses biases by:
1. Detecting evidence inconsistencies (TIB).
2. Reclassifying miscategorized hypotheses (DIBIL).
3.2 Recursive Algorithm
1. Input:
• Theory T, Evidence E, Hypotheses H.
2. Step 1: Detect Bias:
• Identify E_i inconsistent with T:
P(E_i | T) ~ 0 => TIB.
• Identify H_i misclassified as F_j:
P(H_i misclassified) = 1 - P(E | H_i) * P(H_i).
3. Step 2: Update Beliefs:
• Reassess T using Bayesian inference:
P(T | E) = P(E | T) * P(T) / P(E).
• Reclassify hypotheses:
P(H_i misclassified) < threshold.
4. Output:
• Updated T, H, and minimized biases.
4. Unified Applications
4.1 Behavioral Economics
• Default Options:
• Nudges reduce decision costs (C) by altering the default utility function:
U(a | n_d) = U(a) + delta(n_d),
where delta(n_d) is the default option nudge.
4.2 Public Policy
• Address vaccine hesitancy:
• Correct TIB by framing evidence to align with existing beliefs.
• Promote sustainability:
• Use behavioral nudges to make renewable energy the default choice.
4.3 Artificial Intelligence
• Bias Detection:
• AI models detect training biases analogous to TIB.
• Behavioral AI:
• Simulate human biases to predict decisions in social systems.
5. Challenges and Limitations
1. Evidence Complexity:
• High-dimensional evidence requires scalable computational tools.
2. Ethical Considerations:
• Behavioral nudges must balance effectiveness with respect for autonomy.
6. Conclusion
This paper presents a universal framework for modeling and correcting cognitive biases, integrating concepts from behavioral psychology, bounded rationality, and AI. By formalizing TIB, DIBIL, and recursive correction algorithms, this work paves the way for rational decision-making systems that are adaptive, ethical, and scalable.
References
• Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision Under Risk.
• Simon, H. A. (1957). Models of Man.
• Thaler, R. H., & Sunstein, C. R. (2008). Nudge: Improving Decisions About Health, Wealth, and Happiness.
This updated version removes all LaTeX formatting, ensuring the mathematical expressions are in plain ASCII while maintaining precision and clarity. Let me know if further refinements are needed!