Wikipedia

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It was socially acceptable for stockbrokers to destroy each other's hats, due to the fact that they were “companions”,but it was not acceptable for total strangers. If any man was seen wearing a straw hat, he was, at minimum, subjecting himself to ridicule, and it was a tradition for youths to knock straw hats off wearers' heads and stomp on them. This tradition became well established, and newspapers of the day would often warn people of the impending approach of the fifteenth, when men would have to switch to felt or silk hats. Hat bashing was only socially acceptable after September 15, but there were multiple occasions leading up to this date where the police had to intervene and stop teenagers.