Inductive reasoning at the pedestrian crossing

Pedestrians in London have a flexible approach to the lights at pedestrian crossings. If we think we can get across safely, we don’t feel the need to wait for a green light.

If you arrive at the crossing after the pedestrian light has turned red and before the light for the cars turns green, there’s a strange application of the inductive principle that occurs: the longer you wait while it would be clearly safe to cross, the greater your expectation that you could cross safely now. And yet the opposite must be true: for every additional moment that the cars have a red light, their probability of getting a green light in the next moment must be increasing.

I often observe people at traffic lights acting as if they’re reasoning inductively like this. They arrive, wait for a while, and then dash across – often as the light for the cars turns green.

But there are also some alternative possibilities:

Perhaps the Lindy effect is in operation here. If you arrive at the crossing when both lights are red, every additional moment is evidence that this is one of those crossings with a long period of red for both cars and pedestrians.

Or perhaps the pedestrians are responding to a different psychological mechanism. One feels a fool waiting obediently at the curb while others are successfully nipping across. Perhaps there’s an increasing feeling of humiliation, and people wait only as long as their pride can withstand it.