Where did the phrase stool pigeon come from?

One explanation as to how the expression originated is that it arose because hunters of wildfowl in the past used live decoy birds to lure pigeons and other birds within range of the guns. The decoy was tied by a long string to a stool, which the hunter could move about. Thus, "stool pigeon."
By 1830, it was being used in North America to describe a criminal decoy set up by the police to nab other criminals. But by the end of the century, it had come to mean a police informer.