Suppose I am doing random forest classification of labels $A$,$B$,$C$,$D$. There is some theoretical ordering to this output such that when $A$ is more likely than $B$, $B$ is also more likely than $C$, etc. Also, if $P(D) > P(C)$, we also have that $P(C) > P(B) > P(A)$. There are other such conditions that need to be met.
The issue is that a real random forest may give something silly that completely violates the above constraints, even if it is able to predict the most likely outcome successfully. For my use case the ordering is important since decisions are made not only on the most likely outcome.
It also seems intuitive that I should be able to improve generalization if I can somehow enforce this prior knowledge into the model.
How do I account for this in a decision forest? Despite this structure to the output I do not think it is possible to construct a real-valued response variable since they are still class labels with no natural real value, even if there is some type of ordering to them.