How to solve this recurrence

This is not an experiment, as you do not have experimental control (the ability to manipulate an independent variable, or to randomly assign participants to different manipulations). The point of an experiment is to demonstrate causality: that the independent variable determines (at least in part) the dependent or outcome variable. In your case, there is not even a question of causality to be addressed: the participants’ judgements can’t affect the algorithmic rating, and vice versa. What you are seeking to demonstrate is whether there is nonetheless an association between the judgments. ie For a given location, are the answers similar to each other?

So yes, this is simply an observational study, designed to test whether two variables are associated with each other. As there is no causal relationship between them, the terms “independent” and “dependent” variables aren’t ideal. In your case, it might be best to say that you are seeking to determine whether your automated rating is a predictor of the outcome variable, which is the participant judgments. But you could just as validly phrase this in the other direction, and see if the algorithmic ratings differ systematically across values of the human ratings.

Don’t worry that your study can’t be described as an experiment. Entire scientific disciplines (eg a lot of astronomy, anthropology, archaeology) are largely non-experimental.