We study the problem of answering ambiguous web queries in a setting where there exists a taxonomy of information, and that both queries and documents may belong to more than one category according to this taxonomy. We present a systematic approach to diversifying results that aims to minimize the risk of dissatisfaction of the average user. We propose an algorithm that well approximates this objective in general, and is provably optimal for a natural special case. Furthermore, we generalize several classical IR metrics, including NDCG, MRR, and MAP, to explicitly account for the value of diversification. We demonstrate empirically that our algorithm scores higher in these generalized metrics compared to results produced by commercial search engines.