I had input some prediction scores from a learner into the roc_auc_score() function in sklearn. I wasn't sure if I had applied a sigmoid to turn the predictions into probabilities, so I looked at the AUC score before and after applying the sigmoid function to the output of my learner. Regardless of sigmoid or not, the AUC was exactly the same. I was curious about this so I tried other things like multiplication by arbitrary numbers and applying arbitrary log or exp functions and the score was still the same.
Assuming I haven't made some other error somewhere, why is the sklearn function for ROC AUC able to work on any scale of scores?