(1) Higher-order evidence trumps. This is called the 'Equal Weight View' in the peer-disagreement case. In the personal bias case, we might call it the 'Automatic Adjustment View', since it claims you should adjust your initial judgment to compensate for merely possible bias, no matter what the first-order evidence actually recommends. This is essentially the claim that you're in the same epistemic position whether you turn out to be actually biased or not. (After all, the argument goes, from the inside you can't tell which of the two positions you're in. So any rule you can follow will have to treat both situations the same.)
(2) First-order evidence trumps. In the peer disagreement case, this is called the 'Asymmetric No Independent Weight View' -- since the thought is that whoever is actually right about what the first-order evidence supports may thereby "stick to their guns", giving no weight to the opinion of their mistaken peer, but the mistaken person should of course change their opinion to what the evidence really supports. (And too bad if they don't realize this.) This is essentially the claim that learning of possible bias doesn't change your epistemic situation; either the evidence supports P or it doesn't, and your own (in)capacities don't change this fact.
(3) The Total Evidence View. Finally, we might think one is rationally required to take all the evidence into account. Neither first- nor higher-order evidence necessarily trumps the other; though in particular cases it may do so. Note that the inclusion of the first-order evidence introduces some 'asymmetry', but even the correct person may be required to compromise their initial judgment somewhat in light of the (misleading, as it happens) higher-order evidence of their unreliability.
Note that it would seem absolutely bizarre for someone to hold different views about peer disagreement and personal bias. If you think that first-order evidence trumps in case of peer disagreement, it would be terribly inconsistent to suddenly turn around and say the higher-order evidence trumps in case of personal bias. The two issues go hand-in-hand. I'll wrap up this post by noting two further points of correspondence:
(A) The 'equal weight' and 'automatic adjustment' views both gain their plausibility from considering perceptual (more precisely: non-inferential) examples. But this is misleading, because we're effectively imagining a case where there is no (other) first-order evidence; the judgment itself is all we have to go on, so of course unopposed higher-order evidence about the reliability of this judgment is going to be decisive.
(B) Any view which disregards the epistemic importance of first-order evidence is decisively refuted by the problem of implausibly easy bootstrapping. Here I adapt Tom Kelly's objection to the EWV to instead apply to Erica Roedder's automatic adjustment view:
Suppose I receive an incoherent C- paper, and irrationally misjudge it to deserve an A. If the author happens to be a black student and I have evidence that instructors are typically biased against black students, does that automatically mean that all things considered I should boost the grade and give it an A+? Surely not. My initial judgment may be some evidence that the paper warrants an A+. But it's not the only relevant fact. In particular, it can't make up for the fact that the details of the paper itself constitute overwhelming evidence that the paper should be given a C-. The presence of higher-order evidence doesn't excuse me from concluding what the first-order evidence demands.
In short, the AAV (if understood as making positive claims about what I rationally ought to judge) makes it too easy for me to get things right. No matter what loony judgment I initially make, if I then amend it slightly in response to higher-order evidence of bias, then my resulting judgment is guaranteed to be rationally justified! Too easy.
P.S. For background, see Tom Kelly's excellent paper: 'Peer Disagreement and Higher Order Evidence' [pdf].