I didn’t realize this phrase is controversial. TheFreeDictionary defines that phrase as rewards and punishments that influence someone’s behavior, and notes that a long thin carrot may be used because it looks like a stick.
But Boston.com calls this “one of the more vexing language standoffs of our time. Some people say the proper phrase is ‘carrot on a stick,’ meaning an incentive, a carrot dangled in front of a balky donkey. Others are sure it’s ‘carrot and stick,’ suggesting behavior modification by a combination of bribery and threat.”
The “bribery and threat” version is what I grew up with – in New York State – I wonder if the version differs regionally.
Boston.com found an early usage by Lydia Maria Child in 1846, in a widely reprinted story intended to show that children respond better to kindness than to whipping.
“‘I manage children pretty much as the man did the donkey,’ Child’s heroine tells her cranky neighbor, who scolds and beats the young servant girl they share. ‘Not an inch would the poor beast stir, for all his master’s beating and thumping. But a neighbor tied some fresh turnips to a stick, and fastened them so that they swung directly before the donkey’s nose.'”
And also this:
“A [cartoon] image appears in Edward P. Montague’s account of a US expedition to the Dead Sea, published in 1849… One rider is armed with a whip of ‘strong blackthorn twigs,’ which he applies to the animal; the other uses just the bunch of carrots tied to a stick, suspended in front of the donkey.”
Boston.com concludes that “instead of a true version and a mistaken one, then, we seem to have two separate phrases.” They referenced WorldWideWords.
I checked WorldWideWords myself. They report many languages have a version of the phrase, and say it “must have been kicking around informally in English for at least the last century.”
Donkeys are quite smart and have a sense of fair play. I doubt, in real life, a donkey would walk very far trying to eat a carrot that’s always out of reach. I suspect a continuous beating would get you kicked and bitten.
I’ll stick with my childhood version.