Model selection with Gini indices under auto-calibration

The Gini index (Gini score, accuracy ratio) is a popular tool for model selection in machine learning, and there are versions of the Gini index that are used to evaluate actuarial pricing models and financial credit risk models; see Frees et al. [7, 8], Denuit et al. [3], Engelmann et al. [6] and Tasche [17]. However, in general, the Gini index does not give a (strictly) consistent scoring rule; Example 3 of Byrne [1] gives a counterexample.