I have a dataset and I want to design a model to perform a regression. In my dataset, it does not make sense to give each observation a value, but it does make sense to sort them. Can I implement an algorithm to create values for each observation by sorting them?

I thought about this:

1. Select N random observations and sort them
2. Give each observation a new score, equal to its position
3. Calculate the score of an observation as the average position across all times the observation was picked
4. return to step 1

Does it make sense? Is there any machine learning branch that studies this kind of scenarios?

I have a raw unlabeled dataset, and I want to design a model to perform a regression. In my dataset, it does not make sense to give each observation a value, but it does make sense to sort them. Can I implement an algorithm to create values for each observation by sorting them?

I thought about this:

1. Select N random observations and sort them
2. Give each observation a new score, equal to its position
3. Calculate the score of an observation as the average position across all times the observation was picked
4. return to step 1

Does it make sense? Is there any machine learning branch that studies this kind of scenarios?