From my experience, if we chose ignore, they will fade to some degree, but kick around at our heels, nipping like miserably rotten pups.
However, an over exuberant play to their opinions will let them flutter about and talk nonsense until they are filled to their gils with sickness for it. If you allow someone to think they are right, they will carry on with their own smug game and looks until they have had their fill and then be bored with such games and find something else that is new and exciting that they can make wild guesses at.