The Joint Weighted Average (JWA) Operator

Information aggregation is a vital tool for human and machine decision making, especially in the presence of noise and 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 particular 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. Thus far, limited work has sought to integrate both approaches, applying either approach to a different degree. In this paper, we put forward an approach which integrates--rather than partially applies--both approaches, resulting in a novel joint weighted averaging operator. We show how this operator provides a systematic approach to integrating a priori beliefs about the worth of both source and evidence by leveraging compositional geometry--producing results unachievable by traditional operators. We conclude and highlight the potential of the operator across disciplines, from machine learning to psychology.