Excuse the phrasing of the question, but I'm not sure how to put it.
Let's say we know for a fact that Smith is working as a police officer and that police officers have very small salaries. We also know that this causes Smith to lead a lesser life than if police officers were to have larger salaries. When we ask Smith if the government should lower salaries for police officers and raise salaries for firemen, he replies that they should.
I don't think it's correct to say that Smith is unbiased in this scenario, but to say he is biased is misleading. If I were to tell someone that Smith thinks the government should lower police salaries and raise firemen salaries and that Smith is biased, the conclusion would probably be that Smith is a fireman.
So, what is Smith?