A loud bang works and you don't have to aim
I shoot them with a "pea shooter", a cardboard pipe with a balloon attached to one end, loaded with dry lentils or rice. Stretching/charging and releasing the balloon makes a loud, directed thump noise, but by itself it's quickly ignored by pigeons. They need to be actually hit by the load to care. (BTW I can confirm, although quite violent, pigeons seemingly don't readily learn from this experience... They are reall…
That doesn't sound stupid to me. Rather it sounds like they're willing to put with a lot of annoyance in order to get food.