The idea of false consciousness, or that institutions can exert enough power over people to mislead them, is based off of theory of class relations.

The correct answer is Karl Marx's. 
Marx was a famous philosopher and sociologist who was very interested in class relations, so much that he devised his own theory about classes which was studied in schools all over the world for a long time. According to his theory, a person's position in a society is directly determined by their role in the production process.