What type of predictions aim to order cases based on the input variables' relationship with the target?

The correct answer is focused on the concept of ranking, which seeks to arrange cases in a specific order based on how closely they relate to a target variable according to the input variables. In ranking predictions, the goal is not just to categorize or estimate values but rather to establish a hierarchy that reflects the strength or likelihood of the cases in relation to the target. This method is particularly useful when the priority of the cases is important, such as in recommendations or resource allocation scenarios.

Ranking is fundamentally different from classification, which groups cases into distinct categories rather than establishing an order. Similarly, decisions imply a choice or action taken based on the predictions rather than focusing on arranging cases. Estimation refers to predicting a specific numerical value, which does not inherently involve ordering. Thus, ranking is accurately the type of prediction that aligns most closely with the requirement of ordering cases based on relationships with the target variable.