Ordered weighted averaging (OWA) functions, a.k.a. Generalised Gini Index, are routinely used to obtain fair solutions. However, while they ensure some level of fairness in the result, two remaining questions are why they recommend a given alternative, and how robust is this recommendation. We bring practical and theoretically grounded solutions to these questions, by providing an explanation engine for robust OWA that consists in a normative transitive chain of self-evident arguments, themselves based on the normative properties of the model. We provide a thorough theoretical study of the engine, showing that it is sound and complete with respect to the model, with a theoretical upper bound on the length of the explanation and a tractable algorithm (even though minimizing the length is NP-hard). We also provide experimental evidence that the engine performs well on synthetic data. Thus, we guarantee that an explanation can always be found, and that reasoning according to the provided scheme always produces a valid statement. Moreover, the explanations allow to probe the normative requirements of the model, so as to allow validation, accountability and recourse, that are key components of trustworthy AI.