One of the most important challenges in decision theory has been how to reconcile

the normative expectations from Bayesian theory with the apparent fallacies that
are common in probabilistic reasoning. Recently, Bayesian models have been driven
by the insight that apparent fallacies are due to sampling errors or biases in estimating
(Bayesian) probabilities. An alternative way to explain apparent fallacies is by
invoking different probability rules, specifically the probability rules from quantum
theory. Arguably, quantum cognitive models offer a more unified explanation for
a large body of findings, problematic from a baseline classical perspective. This
work addresses two major corresponding theoretical challenges: first, a framework
is needed which incorporates both Bayesian and quantum influences, recognizing
the fact that there is evidence for both in human behavior. Second, there is empirical
evidence which goes beyond any current Bayesian and quantum model. We
develop a model for probabilistic reasoning, seamlessly integrating both Bayesian
and quantum models of reasoning and augmented by a sequential sampling process,
which maps subjective probabilistic estimates to observable responses. Our
model, called the Quantum Sequential Sampler, is compared to the currently leading
Bayesian model, the Bayesian Sampler (Zhu, Sanborn, & Chater, 2020) using
a new experiment, producing one of the largest datasets in probabilistic reasoning
to this day. The Quantum Sequential Sampler embodies several new components,
which we argue offer a more theoretically accurate approach to probabilistic reasoning.
Also, our empirical tests revealed a new, surprising systematic overestimation
of probabilities.