The Asymmetric No Independent Weight View claims that both parties should believe whatever the first-order evidence in fact supported all along. So if you were reasonable in your initial assessment of the evidence, you can reasonably give no weight at all to my (unreasonable, as it happens) opinion.
A third option, Tom Kelly's Total Evidence View, allows that we often should take higher-order evidence into account -- for peer disagreement is evidence that we have evaluated the first-order evidence incorrectly. However, TEV denies that this automatically swamps all first-order evidence. Instead, what's reasonable to believe is determined by one's total evidence (both first- and higher-order, combined).
When put like that, TEV seems clearly right. But it may be unhelpful in practice, if we cannot actually tell where the weight of (first order) evidence lies. Here are some fun cases from last week's epistemology class which put pressure on the view:
Case 1 (ordinary peer disagreement): You and I are expert weather forecasters with the same data set, training, and track record. Nonetheless, we disagree in our current forecasts. Should we revise our judgments on this basis?
Case 2 (chancy curse): As above, but an oracle tells us that long before we were born, a fair coin was flipped which would definitely curse one of us with all the phenomenology of having evaluated the data correctly, but ensure error.
Case 3 (simple curse): As in case 2, but without the coin flip. That is, all we know is that it was determined long ago -- by some unknown method -- that one of us would have all the phenomenology of having evaluated the data correctly, but be guaranteed to make an error.
It seems like the higher-order evidence swamps in case 2, obliging us to split the difference. But then case 3 may seem relevantly similar, and this in turn is effectively no different from case 1 (esp. if determinism is true). So if we want to avoid the Equal Weight View, we must either reject the intuition that we're rationally on a par in case 2, or else explain how to avoid the slippery slope through case 3. Any suggestions?
See also: How Objective is Rationality?