As long as the mashed potatoes doesn't contain any milk or butter or any other meats in the mashed potatoes then the mashed potatoes would be safe to eat when left out overnight.
I've eaten mashed potatoes left out overnight before and it never has made me sick or ill in anyway.
Sometimes I forget to put food like the mashed potatoes away or I have some mashed potatoes left over and have no room in the refrigerator for the mashed potatoes and they've always been still good and safe to eat when left out overnight.
However if you've made the mashed potatoes with milk then I would make sure the mashed potatoes smelled okay as the milk in the mashed potatoes could go sour if left out overnight and then should be thrown out.
I mostly make my mashed potatoes with just water or sometimes chicken broth so it's okay to leave it out overnight.