Individuals make decisions under risk throughout daily life. Standard models of economic decision making typically assume that people evaluate choice options independently. There is, however, substantial evidence showing that this independence assumption is frequently violated in decision making without risk. The present study extends these findings to the domain of decision making under risk. To explain the independence violations, we adapted a sequential sampling model, namely Multialternative Decision Field Theory (MDFT), to decision making under risk and showed how this model can account for the observed preference shifts. MDFT not only better predicts choices compared with the standard Expected Utility Theory, but it also explains individual differences in the size of the observed context effect. Evidence in favor of the chosen option, as predicted by MDFT, was positively correlated with brain activity in the medial orbitofrontal cortex (mOFC) and negatively correlated with brain activity in the anterior insula (aINS). From a neuroscience perspective, the results of the present study show that specific brain regions, such as the mOFC and aINS, not only code the value or risk of a single choice option but also code the evidence in favor of the best option compared with other available choice options.