Human risk preferences are less stable than what economic theories anticipate. Here, drawing from psychological theories of information representation and integration, we predicted and found a novel signature of apparent risk preference reversal in decisions made after experiencing reward information serially: Participants (n = 190, online convenience sample) undervalue high-variance options relative to low-variance ones in independent valuations, consistent with risk aversion; but choose high-variance options more frequently in binary choices, consistent with risk seeking. With three additional experiments we demonstrate that this behavioral gap can be closed but cannot be reversed through manipulating the presentation format (sequential or simultaneous information presentation) and the task demand (absolute or relative judgments). Additionally, aligning presentation format and task demand increases the stability of individual risk preferences across valuation and choice. We conclude that, besides individual differences in risk preferences, taking risks critically depends on cognitive processes of numerosity representation and information integration.