We propose a model of inference and heuristic decision-making in groups that is rooted in the Bayes rule but avoids the complexities of rational inference in partially observed environments with incomplete information, which are characteristic of group interactions. Our model is also consistent with a dual-process psychological theory of thinking: the group members behave rationally at the initiation of their interactions with each other (the slow and deliberative mode); however, in the ensuing decision epochs, they rely on a heuristic that replicates their experiences from the first stage (the fast automatic mode). We specialize this model to a group decision scenario where private observations are received at the beginning, and agents aim to take the best action given the aggregate observations of all group members. We study the implications of the information structure together with the properties of the probability distributions which determine the structure of the so-called "Bayesian heuristics" that the agents follow in our model. We also analyze the group decision outcomes in two classes of linear action updates and log-linear belief updates and show that many inefficiencies arise in group decisions as a result of repeated interactions between individuals, leading to overconfident beliefs as well as choice-shifts toward extremes. Nevertheless, balanced regular structures demonstrate a measure of efficiency in terms of aggregating the initial information of individuals. These results not only verify some well-known insights about group decision-making but also complement these insights by revealing additional mechanistic interpretations for the group declension-process, as well as psychological and cognitive intuitions about the group interaction model.