carrot and stick

Carrot and stick (also spelled "carrot-and-stick") is an idiom used to refer to the act of rewarding good behavior and punishing bad behavior. The carrot represents the edible reward, while the stick refers to a punishing switch. The earliest citation of this expression recorded by the Supplement to the Oxford English Dictionary is to The Economist magazine in the December 11, 1948, issue. The Supplement also depicts a person trying to entice a donkey to move by dangling a carrot in front of it.
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promising to reward or punish someone at the same time The government took a carrot and stick approach to the people who were illegally protesting against the construction of the dam.