By the early 1800s, pigeon came to mean “decoy,” and some decades later, stool pigeon was synonymous with “informer.”
It comes from the practice of using one pigeon to attract other pigeons into captivity.
As anyone who has lived in a big city can tell you, pigeons love to gather in large groups.
Instead of trapping pigeons one at a time, fowlers soon learned it was easier to tether just one to a stool and let it fly and hop around until others came to join the captive bird.
It then became easy to drop a net and capture dozens at a time.