How can I rank preferences without ranking records in a ML model? In a binary classification problem about the purchase of a product I use AUC to evaluate the performance of the model.
Due to some restrictions I can't assign to each record of my data set any metric or even the model's score, but I can compare two different records i.e. I can assign a score to any couple of records.
Are there general methods and/or existing ML models for reconstruct the preferences' ranking without explicitly assigning scores to each record?
 A: Take a look at this link:
https://en.wikipedia.org/wiki/Learning_to_rank
Learning to Rank (LTR) is a class of techniques that apply supervised machine learning (ML) to solve ranking problems. The training data for a LTR model consists of a list of items and a “ground truth” score for each of those items.
There are many machine learning algorithms used for ranking tasks; for example, many of them are used by search engines to rank results of a query. For search engine ranking, this translates to a list of results for a query and a relevance rating for each of those results with respect to the query.
The most famous ranking algorithms are RankNet, LambdaRank and LambdaMART: in all three techniques, ranking is transformed into a pairwise classification or regression problem. That means you look at pairs of items at a time, come up with the optimal ordering for that pair of items, and then use it to come up with the final ranking for all the results.
Even XG-Boost can achieve ranking tasks but literature is full of algorithms to this purpose.
In general, there are three kind of approaches, pointwise, pairwise and listwise. In your case , the most suitable approach seems to be the pairwise one. In this approach, the learning-to-rank problem is approximated by a classification problem, learning a binary classifier that can tell which document is better in a given pair of documents. The goal is to minimize the average number of inversions in ranking.
