偏見，偏私，and 偏心 all seem to mean
biased in some form or another.
Is there a difference among the three, or are they interchangeable?
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偏见 is bias of opinion or concept on different groups, like race groups or religion groups.
偏心 is bias of love on different persons, like children.
偏私 is more used in ancient Chinese and it means bias on people or group to which the subject belongs.
偏见 bias, prejudice
偏私 not impartial (especially when someone is supposed to be impartial)
偏心 (often referring to parents) love one of their children more than others.