Designing Customer Feedback for Subscription Boxes

Problem definition: Subscription box services often ask customers for ratings before choosing what to send. Responses are scarce, and longer questionnaires and finer scales lower completion. We study which candidate items a questionnaire should ask about, and in what format, when the platform then selects a fixed number of them. A design is judged by the expected value lost by not selecting the truly best items. Methodology/results: We approximate each ordinal rating by a Gaussian signal carrying its information at the cutoff between selected and unselected items. As equal numbers of responses per item grow, the ratio of this proxy's loss to the exact loss tends to one. With 1 to 100 responses per item, the two are within about 7 percent. Averaging the information over the prior instead can misstate the loss by about half. For an item far from the cutoff, the value of responses grows slowly at first and then faster, so our envelope rule values responses in blocks. In simulations with a correct prior it lowers the loss by 15 to 81 percent relative to an even spread, and on MovieLens ratings by 6 to 25 percent. Under the proxy, with responses allocated optimally, formats are ranked exactly by one number, the expected information per customer asked. Choosing the format this way comes within about 2 percent of the best on average. Managerial implications: Feedback should go to items whose place in the selection is unclear. Planning helps most when the platform's prior beliefs are informative and right. A platform unsure of its prior should widen it and send the questionnaire in waves. Calibrated on MovieLens ratings, a five-point answer carries about 1.7 times the information of a like/dislike answer, so at equal length the finer scale is better when it cuts completion by less than about 40 percent.