I hypothesize that the chumbox gets populated by items that intersect along the lines of author or tag, ranked by some sort of ‘hotness’ metric (some combination of time since publication, number of recommends, and comments), and that if there are fewer than three items above some arbitrary threshhold cutoff the remaining items are populated using the same mechanism as reading roulette (i.e., hotness plus user’s followed / interacted with tags & authors). I might be way off base, though.
Medium’s particular chumbox is less offensive than outbrain/taboola, and tends to limit itself to mostly articles that genuinely will be interesting to people who read and were interested in the articles. As a result, I wonder if they’re doing something with recomendation-engine-style statistics; after all, they have not only view statistics but read statistics for all articles, not only tags but suggested tags (along with the training data they use to compute suggested tags from content), and full interaction graphs. They have all the information they need to get really excellent suggestion targetting, and (because there’s nothing remotely resembling monetization) there’s no real incentive for people to spend a lot of effort trying to game recommendations.