  In this paper we introduce a novel objective prior distribution levering on
the connections between information, divergence and scoring rules. In
particular, we do so from the starting point of convex functions representing
information in density functions. This provides a natural route to proper local
scoring rules using Bregman divergence. Specifically, we determine the prior
which solves setting the score function to be a constant. While in itself this
provides motivation for an objective prior, the prior also minimizes a
corresponding information criterion.
