The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking and then ordered. This paper describes a new tool for visualizing and displaying ranking information for the weighted rank aggregation method. Traditionally, the aim of rank aggregation is to summarize the information from the input rankings and provide one final ranking that hopefully represents a more accurate or truthful result than any one input ranking. While such an aggregated ranking is, and clearly has been, useful to many applications, it also obscures information. In this paper, we show the wealth of information that is available for the weighted rank aggregation problem due to its structure. We apply weight set decomposition to the set of convex multipliers, study the properties useful for understanding this decomposition, and visualize the indifference regions. This methodology reveals information--that is otherwise collapsed by the aggregated ranking--into a useful, interpretable, and intuitive decision support tool. Included are multiple illustrative examples, along with heuristic and exact algorithms for computing the weight set decomposition.

本文介绍一种新的工具，用于可视化和显示加权排名聚合方法的排名信息。我们使用重量集分解来研究解决这种问题时产生的信息。这种方法可以将聚合排名中被折叠的信息转化成一种有用、可解释、直观的决策支持工具。

带权重排名聚合的权重集分解：一种可解释且视觉化的决策支持工具