In the context of machine learning, for (pre-threshold) model performance metrics, I keep AUPRC and AUROC as my go-to, and then I consider things like a lift curve or cumulative gains chart as a possible handy tool for describing the model to end-users or as a help in defining a threshold.
However, I have an intuition itch that perhaps something like an "area under the lift curve" might also make sense as a performance metric (though I don't see it much discussed). My internal rebuttal initially is that a lift curve is focused on a single target class, but since its calculation includes the ratio of that class to the others, I thought perhaps that isn't a concern.
I'm left without good intuition as to whether or not (and why not if so) an area under the lift curve makes sense. What would be the justification for or against (especially in contrast to metrics like AUROC or AUPRC)?