My prediction that robots will dominate management before they dominate blue collar jobs is based on The Dilbert Principle which observes that the least skilled employees are promoted to management. You need your most skilled people doing interface design, engineering, and the hard stuff. Management is mostly about optimizing resource allocation, and that is something a robot can learn relatively easily, at least compared to most skilled jobs.

Another advantage: the robot manager "can be a hard-ass jerk as often as that is called for":