Question

"members of which ideology would have believed that some people were simply destined to be poor and controlled by the wealthy?"

Answer 1

Social Darwinism--this group believed that some people were fit to rule or have power and others were fit to work for the more powerful. 

This thinking also tends to believe in free market capitalism meaning no government regulation or welfare for the economic system. Social Darwinist thinking excuses the inequality as a natural consequence of the predetermined system.