Existing research shows that the order in which evidence arrives can bias its evaluation and the resulting decision in favor of information encountered early on. We used eye-tracking to study the underlying cognitive mechanisms in the context of incentivized financial choices based on real world market data. Subjects learned about the presence/absence of a transaction fee, before seeing expert opinions regarding an investment prospect and deciding whether to invest. Although the fee had no effect on the processing of negative opinions, we found that positive ones were processed more effortlessly (with lower gaze duration and pupil dilation) when it was absent, that is, when they were congruent with the positive initial information in the shape of the lack of fees. Despite their more effortless processing in the absence of fees, positive opinions then had a greater impact on the subjects' beliefs. In addition to an initial study with 100 subjects, these findings were replicated in a second, preregistered experiment with 103 subjects, in which a positive premium was paid in the event of no fee. Thus, we argue that the valence asymmetry in favor of positive information observed in evaluative priming, person perception, and related tasks (the density hypothesis) also plays a crucial role in incentivized economic choice. In fact, rather than being a detrimental bias, the overweighting of initial evidence often observed in decisions could be seen as an adaptive heuristic aimed at reducing the cost of processing later, similar information.