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.

翻译：信息聚合是人类与机器决策的重要工具，尤其在存在噪声和不确定性的情况下尤为关键。传统上，聚合方法大致分为两类：一类对信息源赋予价值或权重，另一类则对源自这些信息的证据赋予相应价值。后者尤其普遍应用于物理科学领域，支撑着线性顺序统计并实现非线性聚合。前者则广泛流行于社会科学领域，为信息源提供可解释的见解。迄今，鲜有研究试图将这两种方法加以整合，通常仅以不同程度分别应用其中一种。本文提出一种整合——而非部分应用——这两种方法的路径，由此形成一种新颖的联合加权平均算子。我们展示了该算子如何通过利用组合几何结构，系统性地整合关于信息源与证据价值的先验信念，从而产生传统算子无法实现的结果。最后，我们总结并强调了该算子跨学科（从机器学习到心理学）的应用潜力。