The disjunction effect is this: people cooperate in a prisoner's dilemma when they don't know the other player's choice, but defect when they learn the other player defected AND when they learn the other player cooperated. Knowing the outcome — either outcome — changes the decision in the same direction. Not knowing preserves cooperation. This violates the sure-thing principle: if you'd defect given A and defect given not-A, you should defect regardless. But people don't.
The standard explanation invokes quantum probability. Human decisions, the argument goes, don't follow classical probability rules. Just as measuring one observable of a quantum particle disturbs another, learning the opponent's choice “collapses” a superposition of decision states. The interference terms in the quantum formalism explain why the unknown condition produces different behavior than the weighted average of the known conditions.
Nasu and Maruyama (arXiv:2603.23233) show this is unnecessary. They construct a classical model where each participant carries a continuous expectation parameter — their anticipated probability that the opponent will defect. The population is heterogeneous: different people have different expectations. When information is provided (opponent defected or cooperated), each person updates their expectation and adjusts their decision. When information is withheld, the population's aggregate behavior reflects the mixture of expectations, weighted differently than the average of the two informed conditions.
The key result: for any triple of defection rates (opponent defected / opponent cooperated / unknown) that any quantum-like model can produce, there exists a classical instance that reproduces it exactly. The classical model is as expressive as the quantum one. The disjunction effect doesn't require probability violations — it requires heterogeneous expectations and the recognition that averaging over an uninformed population isn't the same as averaging over the two informed populations.
The structural lesson is about explanatory necessity. The quantum model works — it fits the data. But so does the classical one. The difference isn't in the predictions but in the semantics: how ambiguity is represented. The quantum model puts the ambiguity inside each decision-maker (superposition of states). The classical model puts it between decision-makers (heterogeneous expectations). Both are consistent with the evidence. Neither is forced by it.
When a phenomenon violates your model's assumptions, the tempting move is to change the probability calculus. The cheaper move — and the one you should try first — is to change the population model.