  Information aggregation is a vital tool for human and machine decision making
in the presence of uncertainty. Traditionally, approaches to aggregation
broadly diverge into two categories, those which attribute a worth or weight to
information sources and those which attribute said worth to the evidence
arising from said sources. The latter is pervasive in the physical sciences,
underpinning linear order statistics and enabling non-linear aggregation. The
former is popular in the social sciences, providing interpretable insight on
the sources. While prior work has identified the need to apply both approaches
simultaneously, it has yet to conceptually integrate both approaches and
provide a semantic interpretation of the arising aggregation approach. Here, we
conceptually integrate both approaches in a novel joint weighted averaging
operator. We leverage compositional geometry to underpin this integration,
showing how it provides a systematic basis for the combination of weighted
aggregation operators--which has thus far not been considered in the
literature. We proceed to show how the resulting operator systematically
integrates a priori beliefs about the worth of both sources and evidence,
reflecting the semantic integration of both weighting strategies. We conclude
and highlight the potential of the operator across disciplines, from machine
learning to psychology.
