The partial information decomposition (PID) framework is concerned with decomposing the information that a set of random variables has with respect to a target variable into three types of components: redundant, synergistic, and unique. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. Recently, Kolchinsky proposed a new general axiomatic approach to obtain measures of redundant information, based on choosing an order relation between information sources (equivalently, order between communication channels). In this paper, we exploit this approach to introduce three new measures of redundant information (and the resulting decompositions) based on well-known preorders between channels, thus contributing to the enrichment of the PID landscape. We relate the new decompositions to existing ones, study some of their properties, and provide examples illustrating their novelty. As a side result, we prove that any preorder that satisfies Kolchinsky's axioms yields a decomposition that meets the axioms originally introduced by Williams and Beer when they first propose the PID.

翻译：部分信息分解（PID）框架旨在将一组随机变量相对于目标变量的信息分解为三种类型：冗余、协同和独特。经典信息论本身并未提供唯一的方法来进行此类信息分解，因此需要引入额外的假设。最近，Kolchinsky提出了一种基于信息源之间序关系（等价于通信信道之间的序关系）的通用公理化方法，用于获取冗余信息的度量。本文利用这一方法，基于信道之间的经典预序，引入了三种新的冗余信息度量（及其产生的分解），从而丰富了PID的研究领域。我们将新分解与现有分解联系起来，研究其部分性质，并通过实例展示其新颖性。作为附带结果，我们证明：任何满足Kolchinsky公理的预序所生成的分解，均符合Williams与Beer在最初提出PID时所引入的公理。