Ranked or Ordered Class Classification
This looks like it could be framed either as Ordinal Regression or Ranking using Discounted cumulative gain

Ordinal regression is useful when you are trying to classify classes that have some inherent order like &quot;Medium&quot;, &quot;Low&quot; and &quot;Very Low&quot;. Used in psychology and marketing extensively it's a fit modeling procedure for this particular problem. The implementation is quite complicated but in a nutshell can be understood as overlapping distributions that can be understood as probabilities of them belonging to said class. R has an Ordinal Regression package.

Another one is Ranking, most machine learning packages include that in the form of Discounted Cumulative Gain which is a measure of rank quality and it is often used to measure effectiveness of web search engine algorithms or related applications. In xgboost it's found as rank:ndcg.

A naive approach but that can be accurate too is a simple multi-class classification. Information about the order will not be included in the algorithm but surprisingly its results are similar in these kinds of problems because the algorithms underneath like neural nets are now quite powerful specially when you have a big dataset.