The Joint Weighted Average (JWA) Operator

TL;DR

This work introduces the Joint Weighted Average (JWA), a novel aggregation operator that jointly represents the worth of information sources and the evidence they produce. Grounded in compositional geometry, JWA constructs joint weights by perturbing convex source weights with convex order weights, enabling a seamless blend of LWA-like source reliability and OWA-like evidence ordering. The authors show that existing hybrids fail to fully merge these two perspectives and demonstrate, both theoretically and empirically, that JWA can outperform other operators in scenarios where both source quality and evidence quality matter. The approach offers a principled, interpretable framework with broad potential applications from machine learning to psychology and explainable AI.

Abstract

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.

Figures (1)

• Figure 1: Performance of operators in aggregating the evidence provided by 10 sources to predict a simulated criterion across different levels of bias and a series of data sets (x-axis), see Table \ref{['tab:variable']}. Note: continuous line for visibility only.