I realise that similar questin is asked here also Softmax regression or $K$ binary logistic regression
But my concern is related to last section of this article from stanford http://ufldl.stanford.edu/wiki/index.php/Softmax_Regression It says decision will depend on mutual exclusivity of classes and if they are mutual exclusive then prefer softmax else k binary classifiers.
Can anyone provide any rigorous explanation for that statement directly relating the criteria of mutual exclusivity of classes to the performance of algorithm, because that article only has given just one line explanation : "This way, for each new musical piece(each class), your algorithm can separately decide whether it falls into each of the four categories."