Belief perseverance refers to the tendency to cling to one's initial belief even after receiving newinformation which contradicts or disconfirms the basis of that belief.
Everyone has triedto change someone's belief, only to have them stubbornly remain unchanged. Fo rexample, you may have had such debates concerning the death penalty, or abortion, orevolution. People tend to hold on to their beliefs even when it appears that they shouldn't
Other /More definition:
Belief perserverance refers to persistence of one's initial conceptions, as when the basis for one's belief is discredited but an explanation of why the belief might be true survives.