Modeling the Disjunction Effect within Classical Probability: A New Decision Process Model and Comparison with Quantum-like Models

A new paper from researchers Ryo Nasu and Yoshihiro Maruyama challenges a foundational idea in modeling human decision-making. The 'disjunction effect,' famously illustrated by the Prisoner's Dilemma, occurs when people make illogical choices that seem to violate the classical law of total probability. This paradox has been a key motivator for developing 'quantum-like' cognitive models, which propose that human thought processes are inherently non-classical. The authors argue this conclusion is premature, stemming from overly rigid assumptions in conventional classical models.

Nasu and Maruyama's new classical model introduces a critical innovation: a continuous parameter representing a person's subjective expectation (e.g., how likely they think their opponent is to defect). By allowing for this gradient of belief and ambiguity, rather than forcing a binary 'certain' state, their model gains expressive power. They mathematically prove that an instance of their classical model can exactly replicate any pattern of observed decision rates—including strong disjunction effects—while strictly obeying classical probability laws. Furthermore, they demonstrate that for any result produced by a standard quantum-like model of the same experiment, an equivalent classical model exists.

The research shows that the core difference between classical and quantum-like approaches is not in their ability to fit data or a 'breakdown' of classical rules, but in their underlying semantics for representing ambiguity and events. In quantum models, ambiguous states are the generic norm, while in this new classical framework, ambiguity is explicitly parameterized. This reframes the debate from a question of which mathematics is 'correct' to one of which representation is more useful or parsimonious for cognitive science.