Up until kids are school age, reasoning skills are not quite as developed as they will be later in life. Therefore, logical thinking may not apply.
But... a healthy swat with the wooden spoon brooks all intellectual boundaries. Pain is universally understood. If the kid does something wrong, and it smarts right where they have some extra padding, the chances are they will be less likely to do the same thing over and over again.
Pavlov's theory isn't just for dogs.
As they grow older, and they show you what their habits and weaknesses are (TV, phone, video games, etc), they will give you all the leverage that you need.

My kids are 10 and 12. They are out of control for their mother. They are well behaved with me.
Mom negotiates, makes "deals", compromises.
They know my plan.
1st time I ask
2nd time I tell.
3rd time... it will be less than pleasant.