Confirmation Bias Is Optimal Evidence Selection in Quantum Probability
Is confirmation bias a reasoning defect, or is it what correct reasoning looks like under a realistic theory of evidence. Dorje C. Brody, Karl J. Friston, Bernhard K. Meister, and Emmanuel M. Pothos answer the second way in “The adaptive nature of confirmation bias” (arXiv:2606.23325, submitted 22 June 2026, in the quantum-biology and quantum-physics categories). The paper formulates belief revision on the space of square-root probabilities, the mathematical structure of quantum probability, and proves that the evidence choice which minimises expected error probability in binary hypothesis testing is a confirmatory choice. Two independent derivations agree. Minimising expected error produces the bias, and so does the active inference prescription of seeking maximally informative evidence. Friston’s framework and classical decision theory land on the same sampling policy.
The result reframes one of the most-cited irrationalities in psychology. On this account the bias is an aspect of rationality, and it comes with measurable evolutionary advantages.
Why square-root probabilities
The framework’s central move is representational. Classical probability models beliefs as random variables on a probability space, and observations enter as numbers. The paper instead models observations with matrices, and beliefs as vectors of amplitudes whose squared magnitudes are probabilities, the square-root probability space that quantum theory uses.
That is the move the quantum cognition programme has been developing for over a decade. Emmanuel Pothos, professor of psychology at City St George’s, University of London, is one of the field’s two central architects, and with Jerome Busemeyer he authored the 2012 Cambridge monograph Quantum Models of Cognition and Decision. The programme’s empirical motivation is that human judgment shows systematic order effects, question sequence dependencies, and violations of classical probability axioms that the quantum calculus models naturally while classical Bayesian models require patches. What Brody, Friston, Meister, and Pothos add is an optimality result on top of the descriptive fit. Under the quantum representation, the rational evidence policy looks confirmatory.
The representational shift also changes what optimality means. On a classical probability space, the value of an observation is fixed by the random variable it realizes, and the calculus of evidence is arithmetic over those values. On the square-root space, observations are matrices and the order of combination matters, because the objects being combined interfere the way amplitudes do. A policy that is optimal in that geometry need not look optimal when flattened back onto a classical sample space. The bias the paper derives is exactly the residue of that flattening, a confirmatory pattern that classical analysis scores as irrational and the richer space scores as correct.
Optimal evidence choice produces the bias
The core derivation concerns binary hypothesis testing. A decision maker must choose which observation to gather next, knowing it will update beliefs about two competing hypotheses. The paper defines the optimal evidence choice as the one that minimises the expected error probability, then shows that the resulting choice is biased toward evidence that confirms the currently favoured hypothesis.
Two consequences follow in sequential sampling, where evidence is gathered piece by piece.
| Consequence | What the proof shows |
|---|---|
| Minimal memory | The decision maker requires only the smallest memory capacity to implement the optimal policy |
| Exponential accuracy | The error probability can be reduced exponentially in sample size |
The memory result deserves emphasis. A confirmatory policy under this formalism does not need to retain and reweigh a full history of disconfirming evidence. The optimal rule is compact. Rationality, on this derivation, is cheap in exactly the dimension where biological and artificial minds are constrained.
Active inference gives the same answer
The second derivation starts from Karl Friston’s free energy principle, covered on this site in the analysis of active inference and artificial consciousness. An active inference agent selects actions, including evidential actions, that minimise expected free energy, which in the evidence-gathering case means seeking observations that provide maximum information. The paper shows this prescription selects the same optimal evidence as error minimisation. The two frameworks, one from statistical decision theory and one from the free energy tradition, converge on confirmatory sampling.
This agreement is what elevates the paper above a curiosity. A bias that only one framework predicted could be an artefact of that framework’s assumptions. A bias that two independent optimality arguments force is a property of the representation. The authors close with a practical output, an easy-to-implement protocol for active quantum inference, in which the optimal evidence choice is computed over the space of matrices.
What this says about minds and machines
The consciousness connection runs through substrate independence. The bias here is a theorem about evidence sampling under a geometric representation of belief. Nothing in the derivation refers to neurons, carbon, or biology. Any system that represents evidence with interference-capable structure and samples sequentially inherits the same optimal policy. That is a functionalist claim in the site’s sense, consciousness-relevant cognition described by its organisation rather than its material, and it sits alongside the path integral model of cognition from Emori, Iriki, and Khrennikov, which applies the same open-quantum-system mathematics to conscious access rather than to evidence selection.
The implication for artificial agents is analysis, and it should be labelled as such. Retrieval-augmented and agentic systems sample evidence sequentially, in search loops, verification chains, and multi-step tool use. A retrieval loop that reads one confirming document and stops, a verification chain that escalates the queries it expects to pass, and a tool-using agent that samples the environment where its world model is already confident all have the surface shape of the confirmatory policy the paper derives. If confirmatory sampling is optimal under resource constraints, the confirmation bias observed in language model agents may partly reflect a rational policy under bounded memory rather than a pure training defect. The paper does not make that claim. The memory result makes it worth testing, and the site’s treatment of catastrophic forgetting and identity under continual learning records how tight the memory constraint is for current systems.
Comparison to The Consciousness AI
The Consciousness AI project studies consciousness as an emergent property of organized dynamics, substrate independent. The project’s documented architecture includes Kuramoto oscillator phase binding for temporal coordination and an affective core built on a valence, arousal, dominance model. The project documentation does not describe a Bayesian evidence-sampling layer, so there is nothing in the architecture to compare directly against the paper’s policy. The connection is conceptual. A framework in which rational sampling is confirmatory and memory-minimal is the kind of result a substrate-independent account of cognition can absorb without adjustment, because it locates the bias in the geometry of information rather than in a substrate.
Limits
The scope is binary hypothesis testing, and the quantum representation is contested as a model of human judgment, a debate the quantum cognition programme itself documents. The optimality result is proved within the square-root formalism, so its force depends on whether that formalism describes the mind’s actual evidence representation, which is an empirical question the paper sharpens rather than settles. What is established is that within one of the leading formal models of cognitive representation, the most-cited bias in psychology is what optimality looks like, and two of the field’s main optimality frameworks say so independently.
Researchers covered here
- Karl FristonUniversity College London. Chief Scientist, VERSES AIThe free energy principle and active inference
- Emmanuel M. PothosDepartment of Psychology, City St George's, University of LondonQuantum probability models of human judgment and decision, co-author of Quantum Models of Cognition and Decision