What cognitive bias is it when an (ideally objective) evaluation is influenced by the prior opinion of another person? 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?
It's an example of the confirmation bias:


  Confirmation bias (...) is the tendency to search for, interpret, favor, and recall information in a way that confirms one's beliefs or hypotheses.


Research has shown that people have a strong tendency to engage in a positive test strategy when investigating a hypothesis (see e.g., Klayman &amp; Ha, 1978). That is, when testing an expectation (such as in your example) they tend to search for confirming, rather than disconfirming evidence. This tendency then results in the kind of confirmation bias you are describing in your example.

References

Klayman, J., &amp; Ha, Y. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94, 211–228. doi:10.1037/0033-295X.94.2.211