We study
calibrated recommendations for users whose attention decays over the course of a ranked list, meaning that not all recommended items receive equal consideration. For a
distributional model of genres, we extend tools from submodular optimization to provide a $(1-1/e)$-approximation algorithm to calibration. For a
discrete model of genres, we show that the natural greedy algorithm is a $2/3$-approximation. Our work thus addresses the problem of capturing ordering effects due to decaying attention, allowing for the extension of near-optimal calibration from recommendation
sets to recommendation
lists.
(This paper incorporates and supersedes our earlier paper on
ordered submodularity.)