Quantum mechanics, Bayes' theorem and the conjunction fallacy

In the present article we consider the conjunction fallacy, a well known cognitive heuristic experimentally tested in cognitive science, which occurs for intuitive judgments in situations of bounded rationality. We show that the quantum formalism can be used to describe in a very simple way this fallacy in terms of interference effect. We evidence that the quantum formalism leads quite naturally to violations of Bayes' rule when considering the probability of the conjunction of two events. Thus we suggest that in cognitive science the formalism of quantum mechanics can be used to describe a \textit{quantum regime}, the bounded-rationality regime, where the cognitive heuristics are valid.

[1]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[2]  J. Hampton,et al.  Disjunction of natural concepts , 1988, Memory & cognition.

[3]  Mermin,et al.  Simple unified form for the major no-hidden-variables theorems. , 1990, Physical review letters.

[4]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[5]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[6]  Riccardo Franco.  Quantum mechanics and rational ignorance , 2007 .

[7]  Daniel N. Osherson,et al.  The conjunction fallacy: a misunderstanding about conjunction? , 2004, Cogn. Sci..

[8]  A. Peres.  Incompatible results of quantum measurements , 1990 .

[9]  A. Tversky,et al.  Thinking through uncertainty: Nonconsequential reasoning and choice , 1992, Cognitive Psychology.

[10]  Mermin Nd.  Simple unified form for the major no-hidden-variables theorems. , 1990 .

[11]  Diederik Aerts,et al.  A Theory of Concepts and Their Combinations II: A Hilbert Space Representation , 2004 .

[12]  W. Heitler.  The Principles of Quantum Mechanics , 1947, Nature.

[13]  R. Gonzalez,et al.  Compositional Anomalies in the Semantics of Evidence , 1995 .

[14]  Diederik Aerts,et al.  Quantum Interference and Superposition in Cognition: Development of a Theory for the Disjunction of Concepts , 2007, 0705.0975.

[15]  E. W. Adams,et al.  Models of Man, Social and Rational: Mathematical Essays on Rational Human Behavior in a Social Setting , 1962 .

[16]  A. Tversky,et al.  Judgments of and by Representativeness , 1981 .

[17]  J. Frank Yates,et al.  Conjunction errors: Evidence for multiple judgment procedures, including "signed summation" , 1986 .

[18]  Diederik Aerts,et al.  LETTER TO THE EDITOR: Quantum aspects of semantic analysis and symbolic artificial intelligence , 2003, quant-ph/0309022.