Understanding how human minds make decisions under risk is a promising and important target for basic scientific research. The dominant theories about risky decision-making assume that decision conflicts are solved by a compensatory process involving a trade-off of probability against payoff, but it is unclear whether these theories actually represent the events that occur when people make a risky decision. Researchers have argued that an individual’s preferential choice can be better described by a non-compensatory process. Based on the computation and conflict hypotheses, the present thesis utilized psychological, neural and economic methods of research and analysis to explore the behavioral and neural mechanisms underlying risky decision-making. In Study 1, by using event-related potentials, we investigated the neurocognitive mechanisms underlying risky choice by contrasting a preferential choice task with an expected value choice task. The ERP data revealed that 1) the computational difficulty, which would be expected to influence a compensatory process, affected the slow wave only when participants were forced to choose the option with the highest expectation; and that 2) the difference in the minimum gains, which would be expected to be influential in a heuristic process, affected the P300 and slow wave when participants were asked to choose the preferred option. Our findings provide neural evidence that preferential choice is not based on an expectation computation and thus raised the question of whether expectation theories can provide an adequate description of individual risky decisions. In Study 2, by contrasting a preferential choice with a judgment-based choice that required a compensatory process using functional magnetic resonance imaging (fMRI), we explored the mechanisms underlying risky decision-making. First, using parametric analyses, we identified the dorsomedial prefrontal cortex (dMPFC) as the specific region in charge of task-related conflict in risky decision-making tasks. We also showed that the dMPFC was activated less when judgment-based choices were being made, implying that the conflict experienced during a judgment-based choice was not as strong as the conflict that was experienced during the preferential choice. Our results provide neural evidence that preferential choice cannot be characterized solely as a compensatory process. Thus, questions were raised about whether existing compensatory theories could adequately describe individual risky decisions. In Study 3, we conducted an fMRI study to explore whether there were separate neural mechanisms for short-run and long-run probabilistic events. We found that vMPFC and PCC were activated less in the P bet condition than the $ bet condition in the single-play preferential choice task, but reverse in the expected value choice task. We also found individual difference in the multiple-play preferential choice task. Overall result implied that the compensatory rule is more compelling in multiple-play situations. In sum, our results provide behavioral and neural evidence that preferential choice cannot be characterized solely as a compensatory process. We hope our findings could potentially lead to a better understanding of the underlying mechanism of risky decision-making, which could present important directions for future research.