Weighing each label in multi-label classification
Yes, of course, this technique exists. In XGBoost, for instance, you can change the objective function to the multi:softprob which in specifics does:


  multi:softprob: same as softmax, but output a vector of ndata *
  nclass, which can be   further reshaped to ndata * nclass matrix. The
  result contains predicted probability of each data point belonging to
  each class.


From my memory, if it answers your question I think it rounds up to 1.