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

- Takayuki Miyadera,
*Kyoto University*
- Steven Phillips,
*National Institute of Advanced Industrial Science and Technology*

## Abstract

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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