Weight Set Decomposition for Weighted Rank Aggregation: An interpretable and visual decision support tool

TL;DR

This paper introduces a visualization tool for weighted rank aggregation that decomposes weight sets to reveal detailed ranking information, enhancing interpretability and decision support.

Contribution

It proposes a novel weight set decomposition method for weighted rank aggregation, enabling visualization of indifference regions and improving interpretability.

Findings

Reveals detailed ranking information through weight set decomposition

Provides visualizations of indifference regions in weight space

Offers heuristic and exact algorithms for decomposition

Abstract

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.