  Many applications motivate the distance measure between rankings, such as
comparing top-k lists and rank aggregation for voting, and intrigue great
interest to researchers. For example, for a search engine, the use of different
ranking algorithms may return different ranking lists. The effect of a ranking
algorithm can be estimated by computing the distance (similarity) between the
result ranking it returns and the appropriate ranking people expect. People may
be interested in only the first few items of result ranking, therefore the
metric for measuring the distance should emphasize on the items in higher
positions. Besides, in an extreme case, if a result ranking is the total
reverse of the expected ranking, then it is considered to be the worst ranking
with the maximum distance. Therefore, a metric is called for, which can satisfy
both of the two intuitions. To address this problem, we present a weighted
metric based on the classical Spearman's footrule metric to measure the
distance between two permutations of n objects. This metric can be applied in
rank aggregation problem with a polynomial time algorithm, and produces a
2-approximation for adopting the weighted Kendall's tau distance proposed by
Farnoud et al.
