A Loosely Symmetric Model of Cognition

Cognitive biases explaining human deviation from formal logic have been broadly studied. We here try to give a step toward the general formalism still missing, introducing a probabilistic formula for causal induction. It has symmetries reflecting human cognitive biases and shows extremely high correlation with the experimental results. We apply the formula to learning or decision-theoretic tasks, n-armed bandit problems. Searching for the best cause for reward, it exhibits an optimal property breaking the usual trade-off between speed and accuracy.