Good lord. Do I have to explain everything?? It’s not “carrot or stick”. It’s “carrot AND stick”. The phrase “carrot and stick” is not meant to imply a choice between pain and pleasure. It is meant to suggest motivation by the placement of a reward that is always just beyond reach. It’s motivation for donkeys, oxen, and the physics challenged. And the talking heads who read news in front of cameras.
This is what is meant by "carrot and stick"
Lamentations on Chemistry 
For the reward/pain setup, go with “The Drill, or Oil of Cloves?” (Is it safe?)
My tooth aches just thinking about it.
Another reason why vegetarianism is evil. No decent person would pursue salad.
I’ve finally figured out that I’m a atheist vegetarian anarchist scientist. Not sure what I’ll pursue today.
I think “carrot or stick” comes from trying to get a mule or horse to move. You either whack it with a stick or dangle that carrot out in front to get movement. It is akin to the multitude of phrases about alternative of one good versus one bad to get something to happen – “good cop, bad cop” in interrogations, sugar versus vinegar, et cetera.
Perhaps we treat “the carrot or the stick” like the expression (I think) “silver or lead”, but that would leave a lot of Mexican and Colombian immigrants in cold sweats.
Please capitalize the L in Lord
God Bless All
Dear Lord, protect me from your followers.