Outlier detection (OD) is a widely studied problem whose goal is to identify points from a data set that are considered anomalous. Among the methods used in AI and data science, OD is perhaps the most controversial as common applications such as credit card fraud, cyber-intrusion and terrorist activity all involve suggesting that someone is committing a serious crime. However, there is little work on fair outlier detection. We show how to determine if an outlier detection algorithm’s output is fair with respect to multiple protected status variables (PSVs) by formulating various combinatorial problems which attempt to find an explanation (using the PSVs) that differentiates the outlier group from the normal group. We argue that if there is no solution for these explanation problems, then the output of an algorithm can be considered fair, and give a probabilistic interpretation of our work. Since we prove that the underlying combinatorial problems are computationally intractable (i.e., NP-hard), our approaches cannot be efficiently gamed/side-stepped.