Proofs.

We study the role of attention and working memory in choices where options are presented sequentially rather than simultaneously. We build a model where a costly attention effort is chosen, which can vary over time. Evidence is accumulated proportionally to this effort and the utility of the reward. Crucially, the evidence accumulated decays over time. Optimal attention allocation maximizes expected utility from final choice; the optimal solution takes the decay into account, so attention is preferentially devoted to later times; but convexity of the flow attention cost prevents it from being concentrated near the end. We test this model with a choice experiment where participants observe sequentially two options. In our data the option presented first is, everything else being equal, significantly less likely to be chosen. This recency effect has a natural explanation with appropriate parameter values in our model of leaky evidence accumulation, where the decline is stronger for the option observed first. Analysis of choice, response time and brain imaging data provide support for the model. Working memory plays an essential role. The recency bias is stronger for participants with weaker performance in working memory tasks. Also activity in parietal areas, coding the stored value in working, declines over time as predicted.