  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.
