On the Extension of the Elementary Theory of Probability for Psychological Phenomena

Based on a review of the achievements of quantum mechanics and the psychology of perception, some of their possibilities for expanding the classical theory of probability to the field of representing psychological events, for which a combination of outcomes may have a probability greater than the probability of single events from their common set, are considered. It is noted that a model based on a common space of elementary non-intersecting elements is insufficient for describing the psychology of behavior associated with generative processes and co-represented phenomena. To extend elementary probability theory, results from quantum theory relating to ideas about test spaces and the possibility of combining individual events in a test can be used. The proposed models can include both systems of individual tests with repetition of events in additional tests and the possibility of combining individual test events themselves using combinatorial and geometric (projection) methods. Simple examples of expanding classical probabilistic models show that the "Conjunction Fallacy" in the psychology of heuristic behavior should be considered not so much an error of subjects as a scientific illusion of researchers, when they try to fit the behavior of a more complex system into the Procrustean bed of an overly simple model.

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