where rel j,k is the relevance (1 or 0) of the rank k question for j ∈ J. Measurements of serendipity have been established in the context of evaluating recommendation systems (Ge et al., 2010;Shani and Gunawardana, 2011).
(Ge et al., 2010) evaluates serendipity as the ratio of unexpected but relevant results based on a benchmark model that generates expected recommendations, which are relevance-pursuing results.