# WIRE: A Weighted Item Removal Method for Unsupervised Rank Aggregation
## 2 Related Work  
The need for designing fair elections is quite old and has attracted the attention of researchers many decades ago. The Borda Count [14] and Condorcet criterion [15] are among the oldest rank aggregation methods that have been introduced for this purpose. Nowadays, rank aggregation has numerous applications in a wide variety of research areas, including information retrieval, bioinformatics, ballots, etc. [16; 17; 18]. In [19], [PERSON] et al. introduced four rank aggregation methods based on Markov chains to combine rankings coming from different search engines. Originally proposed to combat spam entries, the four methods are derived by considering different forms of the chain's transition matrix. Similarly, [PERSON]. [20] adopted a Markov chain framework to compare the results of multiple microarray experiments expressed as ranked lists of genes. The robust rank aggregation method of [21] proposed an unbiased probabilistic technique to process the results of various genomic analysis applications. More specifically, it compared the actual ranking of an element with the ranking provided by a null model that dictated random ordering. This strategy renders it robust to outliers, noise, and errors. On the other hand, the order-based methods examine the relevant rankings of the items in the input lists, assigning them scores based on their pairwise wins, ties, and losses. The Condorcet method was among the first approaches to adopt this logic [15]. Similarly, the well-known Kemeny-Young method is based on a matrix that also counts the pairwise preferences of the rankers [22; 23]. Then, it uses this matrix to assign scores to each possible permutation of the input elements. Its high computational complexity--the problem is NP-Hard even for four rankers--rendered it inappropriate for datasets having many input lists. More recently, the outranking approach of [24] introduced four threshold values to quantify the concordance or discordance between the input lists. The aforementioned methods have been proven to be quite effective in a variety of tasks. However, they do not take into consideration the level of expertise of the rankers who submit their preference lists. Consequently, they are prone to cases where a ranker may attempt to manipulate the output ranking by submitting spam entries, or simply, to rankers with different importance degrees. The work of [PERSON] et al. proposed a solution that optimized the weighted distances among the input lists [25]. Based on the traditional Footrule distance, the authors established a function that combined the list weights with the individual scores that were assigned to each element by its respective rankers. However, in many cases, these scores are unknown (that is, they are not included in the input lists); therefore, the distance computation is rendered intractable. The weighted method of [PERSON] et al. modeled the problem by constructing preference relation graphs [26]. The list weights were subsequently computed by verifying the validity of several custom majoritarian rules. Furthermore, [PERSON] et al. introduced another weighted technique for crowd opinion analysis applications by adopting the principles of agglomerative clustering [27]. More recently, an iterative distance-based method called DIBRA was published in [13]. At each iteration, DIBRA computes the distances of the input lists from an aggregate list that is derived by applying a simple baseline method like the Borda Count. The lists that are proximal to the aggregate list are assigned higher weights, compared to the most distant ones. This process is repeated until all weights converge and the aggregate list is stabilized. Interestingly, [PERSON]. [13] also introduced the idea of exploiting the learned weights to limit the contribution of the weakest rankers in the formulation of the aggregate list. In particular, the number of elements that participate in the aggregation process is determined by the weight of the respective preference list.