What amount of evidence would have to be produced in order for someone to change their mind?

A mature analysis that is evidence based, reproducible and actionable should change minds yet I’ve often found it entrenches the opposition more because everyone thinks they founded their beliefs on the basis of evidence. No one believes apriori that they are wrong.

I believe as Sheldon Solomon and Ernest Becker have observed:

The Worm at the Core: The existence of others who do not share our beliefs about reality are fundamentally threatening. Anytime we accept the validity of an alternative conception of reality, we undermine the confidence in own beliefs and thus the existence of data which is different than our beliefs really threatens us because it presents empirical evidence that our beliefs might be wrong. Fruits from the tree of science are apt to contain many worms and potential despoilers to one’s own happiness. Think about how you feel when you are wrong.

Philosopher Peter Boghossian – What Would It Take To Change Your Mind?