I'm looking for the name of the cognitive bias that describes the following phenomenon:
Person A asks person B to evaluate and give feedback on a certain topic (a student, a manuscript etc), casually warning person B that the student/manuscript is not very good and so the task will not be particularly pleasant. Person B then tries to objectively do the evaluation, however inadvertently and unavoidably gravitates towards person A's premise, and subsequently has a hard time deciding whether the fact that he too now thinks the student/manuscript is poor is in fact his own opinion or just a regurgitation/confirmation of what person A told him.
First it seemed to me that this is an instance of the hindsight (knew it all along) bias, but I don't think it is, as there the extra (bias inducing) information comes after person A's appraisal, rather than before as is the case in the scenario I describe.
Any other cognitive biases this could be an instance of?