Right and Wrong are mutually acknowledged peers considering whether P. At t0, Right forms 0.2 credence in P, and Wrong forms a 0.8 credence in P. The evidence [E1] available to both of them actually supports a 0.2 credence in P. Right and Wrong then compare notes, and realize they disagree. (Christensen, p.3)
What credence should Right and Wrong then settle on? One version of the Equal Weight View would have them 'split the difference' and settle on 0.5. But, as Tom Kelly has objected, this seems to neglect the first-order evidence entirely. The higher-order (psychological) evidence is equally balanced between .2 and .8, so if we add in the first-order evidence (which supports .2), this should presumably tilt the balance of evidence to something less than .5.
In 'Disagreement, Question-Begging and Epistemic Self-Criticism' [pdf], David Christensen offers a novel response to this objection. He suggests that there's an important asymmetry between the evidence available to the two agents. Basically, the idea is that we get higher-order evidence from other people's judgments, since they can act as 'checks' on our own conclusions; but it would be double counting to treat one's own judgments in the same way. (Just imagine: "E supports .2 credence in H; plus, I just judged that this is so -- all the more reason to give H .2 credence!") Or, as Brian Weatherson might put it, the first-order evidence subsumes whatever evidential force is had by the psychological fact of one's own judgment (regarding that very evidence).
As Christensen points out (p.10), this has very interesting consequences for the case of Right and Wrong:
the important determinants of what's rational for Right to believe are the original evidence E1 (which should, and does, move her to put 0.2 credence in P), and Wrong's dissent (which does and, according to the Equal Weight Conciliationist, should move her from 0.2 to 0.5). In contrast, the determinants of what Wrong should believe are E1 (which should move him toward having 0.2 credence in P), and Right's belief (which also should move him toward 0.2).
In other words, Right should be moved by the (alas, misleading) disagreement from 0.2 to 0.5, whereas Wrong should be moved all the way to 0.2, with his initial judgment counting for naught.
This is interesting, because it's often assumed that both agents share all the same evidence and hence ought to conclude the same thing. And perhaps the most common alternative view would secure divergence in outcome simply by allowing each agent to stubbornly stick close to their own initial estimates. Christensen's solution, by contrast, introduces a genuine asymmetry between the two agents -- thus doing justice to the first-order evidence -- whilst also requiring each agent to give 'equal weight' to the opinion of their peer, rather than downgrading them in a question-begging manner. He can thus offer intuitively appealing answers to both of the opening questions of this post -- an impressive achievement!