 Imprecise probabilists (van Fraasen, 1990, Levi 1974) respond to these difficulties by denying that an agent’s credences are adequately described by a single probability function. Instead, they propose that a belief state is better represented by a set of probability functions. This set represents a kind of “credal committee,” where each member represents a way of precisifying the probability of every proposition. When new information arrives, each member updates by conditioning in the usual way. Levi requires that the credal set be closed under convex combinations. In other words, if \(p,q\) are members of your credal set then \(\lambda p + (1-\lambda) q\) must also be a member of your credal set, for all \(\lambda \in [0,1]\). According to Levi, convex combinations of \(p,q\) are “potential resolutions of the conflict” between them and “one should not preclude potential resolutions when suspending judgement between rival systems” (Levi, 1980). However, resolving conflicts in this way leads to some unintuitive consequence. For example, if \(p,q\) agree that two events are probabilistically independent, the same is not true of their convex combinations. Furthermore, if all members of the credal committee agree that some coin is biased (because it is bent) but not on the direction of the bias, it is unintuitive to require that some committee member believe that the coin is fair. For more on how to aggregate the opinions of agents with probabilistic credences, see Dietrich and List (2016) and section 10.4 in Pettigrew (2019).