Placebo buttons are buttons that actually do nothing except give the user an illusion of control.
The advent of computer-controlled traffic signals make the walk buttons at pedestrian crossings on heavily trafficked streets obsolete. By the late 1980s, most (but not all) walk buttons in New York City have been deactivated yet people push them anyhow, either in ignorance, out of habit, or in the off chance the buttons did work.
Many large office buildings also have dummy thermostats to give office workers the illusion of control. Some even go as far as installing white-noise generators to mimic the hum of fans after the HVAC system is shut off.
The same goes for the close button in elevators. Most elevators built or installed since the early 1990s don't have close buttons that work, unless you have a fireman's key. People do push them anyhow, because the fact that the door eventually closes reinforces their belief that the button works.