Some things go together like peas and carrots. Others go together like carrots and sticks, which could mean a lot of different things, depending on how you use this phrase.
Our listener Bob Wilkes has heard "carrot and stick" used on NPR to refer to an incentive and a punishment. For example, "If the carrot doesn't work, we may have to resort to more stick." However, that's not the meaning Wilkes knows.
"I first heard the term when I was growing up, and then it referred to a way of getting a horse to pull a wagon, cart, or buggy. Instead of using a buggy-whip, a driver would tie a carrot to a stick and dangle it in front of the horse’s nose," Wilkes says. "So the 'carrot and stick approach' meant finding a way to get someone to do something you wanted them to do, perhaps by tricking them."
Wilkes wanted to know the original meaning of "carrot and stick" and whether its meaning has changed over time. As per usual, Professor Anne Curzan was happy to help.
The Oxford English Dictionary dates the figurative use of "carrot" to describe an enticement or promised reward back to the 19th century. The phrase "carrot and stick" in reference to an incentive and punishment has also been around since at least the 19th century.
On his World Wide Words blog, Michael Quinion notes an example from 1876 as the first we have in print in English. It comes from a Lord Blatchford work called The Reality of Duty: As Illustrated by the Autobiography of Mr. John Stuart Mill and describes a "carrot and stick" approach to child-rearing: "It was this carrot and stick discipline to which Mr. John Mill was subjected, and which he accepted dutifully as flowing from that perfect wisdom of which up to this time his father had been the representative."
Notice how the author doesn't bother to explain what "carrot and stick discipline" is? That suggests "carrot and stick" was in circulation at the time and people would likely already know what Blatchford meant. Quinion goes on to point out that multiple languages including Italian, Danish, German, and Russian have expressions that translate either exactly as "stick and carrot" or as something very similar, such as "whip and carrot."
Though a carrot can most certainly be used as an incentive or a reward for a horse or other animal, the idea of tying one to a stick and dangling it front of the animal's nose to get it to pull a buggy appears to have been put forward as a joke, as Quinion points out with several examples.
However, it's a joke that goes back to the 19th century.
It would seem then that the two meanings of this phrase that our listener Bob Wilkes wrote to us about likely co-existed. There isn't any evidence though that one was the original and the other was a corruption of it.