"Many [metaphors] are used without knowledge of their meaning... Some metaphors now current have been twisted out of their original meaning without those who use them even being aware of the fact. For example, toe the line is sometimes written tow the line. Another example is the hammer and the anvil, now always used with the implication that the anvil gets the worst of it. In real life it is always the anvil that breaks the hammer, never the other way about: a writer who stopped to think what he was saying would be aware of this, and would avoid perverting the original phrase."—George Orwell, Politics and the English Language (1946)
"Carrot and stick", of course, refers to the old method of getting a horse to pull a plow by dangling a carrot in front of his nose, which is attached to the end of a stick. The correct use of the metaphor would be to mean anytime when someone is motivated by promises of a nonexistent reward. This is almost never how it is actually used, however. Overwhelmingly it is used to refer to a situation where one simultaneously offers a reward and threatens a punishment; apparently the thinking is that one is standing there with a carrot in one hand and a stick in the other, and will give you the carrot if you're good and hit you with the stick in you're bad.
This is nonsensical, and annoying. Why should a carrot represent a universally-desired reward? Plenty of people dislike carrots. Similarly, getting hit with a stick is unpleasant, but I can think of worse things to deal with. My friend Derek suggests we substitute in these instances "delicious cake" and "sack of leeches" for "carrot" and "stick". To my mind, this is much more effective.
This site is an attempt to get people to quit misusing the "carrot and stick" metaphor by publicly humiliating them. Please feel free to send any examples not listed here to me at @unknown.nu.