Aggregating incoherent agents who disagree

We would like to arrive at a single coherent pair of credences in X and X. Perhaps we wish to use these to set our own credences; or perhaps we wish to publish them in a report of the WHO as the collective view of expert epidemiologists; or perhaps we wish to use them in a decision-making process to determine how medical research funding should be allocated in 2018. Given their expertise, we would like to use Amira’s and Benito’s credences when we are coming up with ours. However, there are two problems. First, Amira and Benito disagree— they assign different credences to X and different credences to X. Second, Amira and Benito are incoherent — they each assign credences to X and X that do not sum to 1. How, then, are we to proceed? There are natural ways to aggregate different credence functions; and there are natural ways to fix incoherent credence functions. Thus, we might fixAmira and Benito first and then aggregate the fixes; orwemight aggregate their credences first and then fix up the aggregate. But what if these two disagree, as we will see they are sometimes wont to do? Which should we choose? To complicate matters further, there is a natural way to do both at once — it makes credences coherent and aggregates them all at the same time. What if this one-step procedure disagrees with one or other or both of the two-step procedures, fix-then-aggregate and aggregate-then-fix? In what follows, I explore