FWIW, I worked on a team that built a platform which used customer activity to predict their NPS score. The algorithm was straight-forward and the results were pretty accurate; enough so to be used by A/B testing platforms for testing new features on users. A side-effect of our research was insight into the key features that dictated a positive response. Even with a complicated product, success was highly dependent upon about four of the 200 or so features we collected.

I suspect that the minds at Amazon could come up with a much better solution than what we did. By virtue of having smarter, more experienced people on average, and a more simplistic product.