Why did paying for rat tails leave Hanoi with more rats?

Because the reward paid for rat tails, not for fewer rats, and people found it more profitable to keep rats alive. In 1902, with a plague pandemic raging, the French authorities in Hanoi offered one cent per rat, collected on presentation of the tail. Soon officials noticed healthy rats running around with no tails: hunters were cutting off the tails and releasing the rats to breed more. Then inspectors found farms outside the city raising rats purely for their tails.

Economists call this a perverse incentive: a reward that produces the opposite of what its designers wanted. It's often nicknamed the cobra effect, after a story that British rulers in Delhi paid for dead cobras, people bred cobras for the cash, and when the scheme ended they freed their snakes. That tale may be a legend, though. The historian Michael Vann, who rediscovered the Hanoi episode, argues that the cobra story can't be proven while the rat story can, and suggests calling it the "Rat Effect".

The pattern keeps repeating. A US Army base paid $40 per feral pig tail, and the pig population grew. In 2002 British officials offered Afghan farmers $700 an acre to destroy their poppies, and farmers rushed to plant more. The lesson: reward exactly what you can measure, and people will give you exactly that, even when it's not what you wanted.