Is standard deviation of the output layer probability vector a good proxy of model confidence? I'm working on a multi-classification problem and I'm kinda new to neural networks, which is what I'm using. In the model I'm using now, the probability vector has to sum up to 1, which to me would mean little variation means little confidence. So if I'm on a 3-class classification problem and my output is:
[0.33 0.33 0.33]

There seems to be no confidence on the results, and the standard deviation is zero. On the other extreme:
[1 0 0]

There is a lot of confidence and the standard deviation is maxed out.
Is this approach okay to sort my results by confidence? Is there a better, more standard approach?
What I want to do in the end is to present all new predictions sorted by how confident the model is in its prediction. We can't deal with false positives or negatives, so each prediction has to be manually validated, and thus, it'll be better to sort said results from least confident to more confident, so the people that have to check said results can use most of their focus at the beginning.
Thanks a lot

Generally the "AI/Machine Learning" people don't really view and evaluate error and probability the same way statisticians do. A "standard" way of evaluating this type of model would be with a confusion matrix, which in this case would simply be a 3X3 crosstabulation of all how each data point was classified. This is the "Machine Learning" approach to accuracy: point estimations and correct classification are more important than properly calibrated confidence.
That being said, if you're using a softmax activation function on your final layer, then by definition these are probabilities, or, perhaps more precisely, expected values across a multinomial distribution. So your interpretation is totally valid. This is a more "statistical way" of thinking about the output.
Edit: If we wanted to "sort the cases by confidence" the simplest option would be simply to sort by the variance of the vector of the three outputs. Outputs with high variance mean the model is "less confident" in its answer.
