A Quantum Probability-theoretic account of human judgment using Positive-Operator-Valued Measures


People make logically inconsistent probability judgments. The ``Linda'' problem is a well-known example, which often elicits a conjunction/disjunction fallacy: probability of constituent event A (B) judged more/less likely than their conjunction/disjunction. The Quantum Judgment model (QJM, Busemeyer et al 2011) explains such errors, which are not explainable within classical probability theory. We propose an alternative axiomatic approach in the framework of quantum probability theory that employs positive operators representing the set of general queries, in constast to QJM which uses projection operators. Like QJM, our model accounts for conjunction/disjunction fallacies, averaging type errors, and unpacking effects, suggesting that it provides a viable model of judgement error. Further differences between our model and QJM are also discussed.

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