No search engine is perfect. A typical type of imperfection is the preference misalignment between search engines and end users, e.g., from time to time, web users skip higherranked documents and click on lower-ranked ones. Although search engines have been aggressively incorporating clickthrough data in their ranking, it is hard to eliminate such misalignments across millions of queries. Therefore, we, in this paper, propose to accompany a search engine with an “always-on” component that reorders documents on a perquery basis, based on user click patterns. Because of positional bias and dependencies between clicks, we show that a simple sort based on click counts (and its variants), albeit intuitive and useful, is not precise enough. In this paper, we put forward a principled approach to reordering documents by leveraging existing click models. Specifically, we compute the preference probability that a lower-ranked document is preferred to a higher-ranked one from the Click Chai...