Carrot and stick; Carrot or stick
in
This is about rewarding someone for doing something good, or threatening to punish them if they don’t. The carrot represents the reward, and the stick represents the threat.
She used the old carrot or stick trick with her son to get him to eat the spinach; Some ice cream tonight, or no ice cream for a week!
Compare to:
Carrot on a stick.
History:
Some believe this has to do with mules: There are two ways to get a mule move forward. Dangle a carrot in front of it, or hit it in the back with a stick.