Belief updating in decision-variable space: past decisions with finer granularity attract future ones more strongly

Abstract

When engaged in decision-making tasks, humans are known to create decision variables. Much effort has focused on the cognitive processes involved in forming decision variables. However, there is limited understanding of how decision variables, once formed, are utilized to adapt to the environment. We reason that decision-makers would benefit from updating the belief of decision-variable. As one such belief updating, we hypothesize that a decision commitment restricts the probabilistic belief distribution of decision variable to a range corresponding to that decision. This implies that past decisions not only attract future ones but also exert a greater pull when those decisions are made with finer granularity-- dubbed the granularity effect. Here, we present the findings of seven psychophysical experiments that confirm these implications. Further, as a unified account of the granularity effect, we offer a Bayesian model. Our work demonstrates how humans leverage the decision-variable to effectively adapt to their surroundings.