I am really sick of clueless morons spouting on about "carrots and sticks" and thinking they are channeling folk wisdom with their misuse of the idiom.
The way they use it is totally wrong. They seem to be saying "we'll give you this carrot, but if you don't take it, we will hit you with a stick."
These people are, quite simply, stupid and, frankly, ill-educated.
The "Carrot and Stick" approach is old-time folklore. According to the legend, a farmer had a lazy mule who would not pull the plow. Whipping the mule did not help, so the farmer devised a clever strategy - he got a stick, and tied a carrot to the end and dangled it in front of the mule. The mule wanted the carrot, so he walked toward it, pulling the plow behind him.
But - the farmer never gave the mule the carrot, and the mule caught on and stopped pulling the plow.
The moral of the story is, if you offer rewards, you have to follow through - not that someone is going to whoop your ass if you don't take his carrot.