Bridging the intuition gap in Cox's theorem: A Jaynesian argument for universality

Abstract

Various attempts have been made to patch the holes in Cox's theorem on the equivalence between plausible reasoning and probability via additional assumptions regarding the density of attainable plausibilities (so-called “universality”) and the existence of continuous and strictly monotonic functions for manipulating plausibility values. By formalizing an invariance principle implicit in the work of Jaynes and using it to construct a class of elementary examples, we derive these conditions as theorems and eliminate the need for ad hoc assumptions. We also construct the rescaling function guaranteed by Cox's theorem and thus provide a more direct proof and an intuitive interpretation for the theorem's conclusion.