# WIRE: A Weighted Item Removal Method for Unsupervised Rank Aggregation
## 1 Introduction  
Rank aggregation algorithms accept as input a set of ordered element lists submitted by a group of rankers. Then, they process these lists and return a consensus ranking with enhanced element ordering. Such problems are quite common in numerous research fields, such as bioinformatics [1, 2], sports [3], recommendation systems [4, 5], information retrieval [6, 7, 8], ballots [9, 10], and so forth. Most existing methods consider that input lists are of equal importance. Hence, they do not investigate issues where, for example, a list is submitted by an expert or a non-expert ranker, or a spammer submits a preference list in order to promote or downgrade specific elements. Although this non-weighted approach aligns with several application areas (e.g., fair elections), in other cases, such as collaborative filtering systems, it usually leads to output lists that suffer from bias, manipulation, and low-quality element ranking. In contrast, the weighted rank aggregation methods take the aforementioned issues into account and attempt to assess the input list quality before they fuse them into a single ranking [11, 12, 13]. By applying unsupervised exploratory analysis techniques, they assign weights to the input lists with the aim of evaluating their significance. In the sequel, they exploit these weights during the computation of the scores of the respective list elements. More specifically, the list weights are embodied in the individual element scores, thus affecting their ranking in the output list. In the vast majority of cases, this is how the weighted methods exploit the learned list weights. However, the distance-based method of [PERSON] et al. [13] introduced a more inspiring approach. First, an iterative algorithm was applied to estimate the importance of the input lists by measuring their distances from the generated output list. Then, the distance-based ranker weights were used in two ways as follows: (i) to compute the element scores in a manner that promotes those submitted by expert rankers, and (ii) to prevent low-quality elements submitted by non-expert rankers from entering the final aggregate list. In this context, the learned weights were used to determine the number of elements that each input list contributed to the final ranking. The experiments of [13] demonstrated that weight-based list pruning can yield promising results, especially when the input lists are long. However, for input lists that consist of only a few items, the gains are considerably limited, or even reversed in some cases. These findings indicate that a more sophisticated approach is required to fully exploit the learned ranker weights. To alleviate this issue, this paper introduces a novel, unsupervised method, called WIRE, that regulates the contribution of each input list in the formulation of the aggregate list. In contrast to the suggestions of [13], our strategy does not simply remove elements from the bottom of the input lists, but it carefully removes the weakest elements, with respect to their overall score, from the less important lists, with respect to their weights. In this way, it constructs aggregate lists of improved quality, even when the input preference lists are short. In addition, note that this refinement mechanism depends only on the input lists, the consensus ranking, and the weights of the involved rankers. Since this information is directly accessible either from the input or from the base aggregator, two major advantages of WIRE are derived. First, it fits into any weighted rank aggregation method and can be applied as a post-processing step. Second, its independence from individual element or list attributes (e.g., ranks, scores, lengths, etc.) renders it capable of handling partial rankings. These design choices increase our method's flexibility and applicability. The remainder of this paper is organized as follows. Section 2 provides a brief overview of the relevant literature on weighted rank aggregation.