 Objection 1: Appeal to summation is arbitrary. One concern about Decomposition is this: it is crucial for the proof that the Brier score and only the Brier score satisfies all of Pettigrew’s conditions that in Decomposition we combine the distance between \(c\) and \(c^w\) with the distance between \(c^w\) and \(v_w\) by summing them together. But we could have combined those quantities in other ways: we might have multiplied them together, for instance; or, we might have summed them and then taken a strictly increasing function of that sum. It might be mathematically natural simply to add them together: but that doesn’t privilege that means of combining them for philosophical purposes. However, if we combine them in any of these alternative ways, Pettigrew’s conditions will no longer hold of the Brier score.