The door-close rain dance
The vast majority of the time, the door-close button on elevators doesn’t do anything. This is the case for the elevators in our office building.
When they’re in the lobby, and someone pushes a floor button, the elevators wait for an extra 5 seconds before closing the doors. This is an optimization to accumulate additional passengers — when lots of people are coming in and out of the lobby all the time, you don’t want elevators going up with just one person in them.
Inevitably, people start getting impatient and hitting the door-close button after about 4 seconds. It doesn’t do anything, but the doors close a second or two later regardless, so people think they’ve affected the outcome, and they push the door-close button again the next time. If they push the button too soon, and the elevator waits a few more seconds before closing the doors, the people assume that it’s just being slow today or they didn’t hit the button hard enough.
They never consider the possibility that their action is not related to the result.
This is why superstition works. Animals learn it, too. “If I perform this action, I get this result.” It takes a more advanced or analytical mind to consider performing a test: “If I take no action, will I get this result anyway?”
I secretly think less of door-close people in the elevator.
I openly think less of engineers who insist on putting broken buttons on devices. Especially when there are clear uses for such a button. Sure, stop the function on busy floors (the lobby) or during busy times (rush hour), but if I get off work at 5:30, why should I have to wait the extra seconds for a phantom passenger?
Niggling over a few seconds? Yeah, but then my point is, don’t put the button there in the first place.
The same could be said about the pedestrian “Push to Cross” buttons on Crosswalks. The vast majority of those don’t work. It’s even more aggrivating when it’s necessary. There’s one intersection that changes every 5 minutes, an ETERNITY by comparrison. It still has a “Push to Cross” button, and it obviously doesn’t work. So much for the reassurance the ghost button is supposed to bring.

