I stumbled upon a 3-class classification problem where all compared classifiers yield a higher AUC than accuracy (usually around 10% higher). This happens both when the dataset is balanced or slightly imbalanced.
Now, after looking at this answer: Why is AUC higher for a classifier that is less accurate than for one that is more accurate? I understand that, for binary classification, this might happen because the accuracy is typically computed at a threshold of 0.5 whereas AUC is based on all threshold values.
But what happens with multi-class classification? Specifically, those scenarios where accuracy is defined as the frequency with which the predicted labels match the true labels (tf.keras.metrics.CategoricalAccuracy) and AUC is defined as the weighted average of the AUC for each class vs the rest (One-vs-rest) (sklearn.roc_auc_score). Why might AUC be higher there?
In other words, I'm trying to understand what this result means. Does it mean that my classifiers can discern well when each class is measured against the others (AUC), but not as well when the prediction probabilities are an output of the softmax function, and therefore spread out for the three classes?