Blaise Pascal's 350-year-old trick to get people to change their minds is now backed up by psychologists. Pascal suggests that before disagreeing with someone, you should first point out the ways in which they’re right. And to effectively persuade someone to change their mind, you should lead them to discover a counter-point themselves, at their own pace.
In Pascal's words:
When we wish to correct with advantage, and to show another that he errs, we must notice from what side he views the matter, for on that side it is usually true, and admit that truth to him, but reveal to him the side on which it is false. He is satisfied with that, for he sees that he was not mistaken, and that he only failed to see all sides. Now, no one is offended at not seeing everything; but one does not like to be mistaken, and that perhaps arises from the fact that man naturally cannot see everything, and that naturally he cannot err in the side he looks at, since the perceptions of our senses are always true.
And Pascal also added:
People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others.
This is also somewhat like the Skinner method, where you keep agreeing with them until they see...Pascal is telling us to first get them to lower their defences and prevent them from digging their heels in to the position they already staked out.
This is also like the the Socratic Method. Socrates asked universal questions that resulted in a 'yes' answer, leading around to the subject matter where they almost have to admit they are wrong.
Pascal's method 'nudges' the other party to see the truth, in their own time, in their own way.