  We propose a new notion of uniqueness for the adversarial Bayes classifier in
the setting of binary classification. Analyzing this concept produces a simple
procedure for computing all adversarial Bayes classifiers for a well-motivated
family of one dimensional data distributions. This characterization is then
leveraged to show that as the perturbation radius increases, certain the
regularity of adversarial Bayes classifiers improves. Various examples
demonstrate that the boundary of the adversarial Bayes classifier frequently
lies near the boundary of the Bayes classifier.
