Abstract
Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence (PIE) Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set‐based credal judgment to frame and address a range of subtle issues that arise in peer disagreements.
1. Reasonable Range
You and a colleague hold different beliefs on the truth of the proposition that it will rain tomorrow in Riga. You think it is likely to rain. Your colleague believes otherwise. Neither you nor he can claim an epistemic advantage about the matter. You have the same evidence. The same level of expertise. The same powers of reasoning. You are epistemic peers. Upon learning that you have a disagreement with an epistemic peer, should you revise your beliefs? Should he? If so, how?
One response to an epistemic peer disagreement—or simply, peer disagreement—is to be conciliatory with your epistemic equals by adopting a new belief that assigns to each opinion in the disagreement equal weight (Elga 2007, p. 484) thereby splitting the difference (Christensen 2007, p. 203).1 There are at least two versions of the equal‐weight response, however, which engender different assumptions about the nature of the evidence a peer disagreement generates, and how that evidence should guide a peer to change her view.
According to most proponents of the equal‐weight view a peer disagreement delivers to you evidence that either you or your peer is mistaken about the proposition in dispute. So, one version of the equal‐weight view has it that the evidence from a peer disagreement is undermining in character and therefore that your reaction to a peer disagreement ought to be the same as your reaction to receiving any other new but conflicting piece evidence: you ought to suspend judgment on the proposition until additional evidence is gathered (Feldman 2010).
If belief is interpreted categorically, suspending judgment on a disputed proposition amounts to neither believing it nor its negation. If instead belief is interpreted partially, and in particular is representable by a unique real‐valued probability function, then suspension of judgment typically amounts to assigning a partial belief of 1/2 to the proposition in question. Either way, the motivation for suspending judgment is the same. Since the evidence that one receives from a peer disagreement is taken to undermine rather than ameliorate one’s current view, suspension‐of‐judgment versions of the equal‐weight view are guided by the notion that one ought to respond to a peer disagreement by increasing one’s uncertainty about the proposition in dispute.
Another version of the equal‐weight view counsels against suspending judgment. On this version a peer disagreement supplies you with a range of informed opinions, including your own, so you ought to exploit this information to improve upon your current judgment. Here the evidence from a peer disagreement is taken to be ameliorative in character, so one ought to respond by taking the equally‐weighted average of the set of peer judgments as one’s new partial belief (Douven 2010).2
One advantage opinion pooling strategies have over a naïve suspension of judgment is that pooling strategies in general, and equally‐weighted averaging in particular, yield a new partial belief that is guaranteed to fall within the reasonable range of informed opinions.
- Reasonable Range Principle: For any group of peers,
, whose partial beliefs in a proposition A range from x, the lowest confidence in the truth of A expressed by a member 
, to y, the highest confidence in the truth of A expressed by a member of 
, a new belief is said to be within the reasonable range for members of 
if and only if its value is within the closed interval 
.
To motivate why the Reasonable Range Principle is reasonable and a policy of naïve suspension of judgment is not, imagine that your degree of belief in rain tomorrow in Riga is 8/10 but your epistemic peer’s is 9/10. Upon learning of this disagreement it would be foolish to advise either you or your peer to naïvely suspend judgment by adopting a partial belief of 1/2 that it will rain tomorrow. After all, you both agree that it is more likely to rain in Riga than it is for a fairly tossed coin to land heads, and no strategy to resolve a disagreement among peers should mandate that each ought to suspend judgment on a proposition they both believe is overwhelmingly more likely to be true than false. Whatever uncertainty this peer disagreement may introduce, it should not wipe out this point of agreement.