Recent advances in artificial intelligence offer many beneficial prospects. However, concerns have been raised about the opacity of decisions made by these systems, some of which have turned out to be biased in various ways. This article makes a contribution to a growing body of literature on how to make systems for automated decision-making more transparent, explainable, and fair by drawing attention to and further elaborating a distinction first made by Nozick between first-level bias in the application of standards and (...) second-level bias in the choice of standards, as well as a second distinction between discrimination and arbitrariness. Applying the typology developed, a number of illuminating observations are made. First, it is observed that some reported bias in automated decision-making is first-level arbitrariness, which can be alleviated by explainability techniques. However, such techniques have only a limited potential to alleviate first-level discrimination. Second, it is argued that second-level arbitrariness is probably quite common in automated decision-making. In contrast to first-level arbitrariness, however, second-level arbitrariness is not straightforward to detect automatically. Third, the prospects for alleviating arbitrariness are discussed. It is argued that detecting and alleviating second-level arbitrariness is a profound problem because there are many contrasting and sometimes conflicting standards from which to choose, and even when we make intentional efforts to choose standards for good reasons, some second-level arbitrariness remains. (shrink)