Error is Lawful: A First-Principles Theory of Counterfactual Bias

Counterfactual thinking shapes learning, blame, and choice. Yet people’s judgments are systematically biased, and current theories describe only that they err, not why. Here we demonstrate that these biases are not reasoning failures, but the inevitable output of a system operating under fundamental constraints. Testing this claim across 10,000 simulations—spanning diverse causal graphs and cognitive profiles—yields precise results: information loss occurs exactly when causal width exceeds processing capacity; memory noise accumulates lawfully with depth; and overall bias follows a multiplicative form, fitting the data with near-perfect accuracy. These findings transform how we understand rationality: what looks like irrational error is actually lawful behavior under constraint—with direct implications for law, medicine, and policy.