https://en.m.wikipedia.org/wiki/Carrot_and_stick
The "carrot and stick" approach (also "carrot or stick approach") is an idiom that refers to a policy of offering a combination of rewards and punishment to induce behavior. It is named in reference to a cart driver dangling a carrot in front of a mule and holding a stick behind it. The mule would move towards the carrot because it wants the reward of food, while also moving away from the stick behind it, since it does not want the punishment of pain, thus drawing the cart.
The idiom is used in the field of International Relations to describe the realist concept of 'hard power'. The carrot can stand for tax cuts or other benefits, the stick can stand for the use of (psychological) violence and threats by the government.
In modern usage, the idea has also come to be used in a related idiom, "the carrot or the stick." This refers to the process of weighing and/or deciding whether a desired behavior would be better induced via the enticement of benefits or the threat of punishments.[1]
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. Earlier uses of the expression were published in 1947 and 1948 in Australian newspaper commentary discussing the need to stimulate productivity following World War II.[2][3] An earlier American example was published in February 1948 in a Daily Republic newspaper article discussing Russia's economy.[4]