University ranking has become an important indicator for prospective students, job recruiters, and government administrators. The fact that a university rarely has the same position in different rankings motivates us to ask: To what extent could a university’s best rank deviate from its “true” position? Here we focus on 14 rankings of Chinese universities. We find that a university’s rank in different rankings is not consistent. However, the relative positions for a particular set of universities are more similar. The increased similarity is not distributed uniformly among all rankings. Instead, the 14 rankings demonstrate four clusters where rankings are more similar inside the cluster than outside. We find that a university’s best rank strongly correlates with its consensus rank, which is, on average, 38% higher (towards the top). Therefore, the best rank usually advertised by a university adequately reflects the collective opinion of experts. We can trust it, but with a discount. With the best rank and proportionality relationship, a university’s consensus rank can be estimated with reasonable accuracy. Our work not only reveals previously unknown patterns in university rankings, but also introduces a set of tools that can be readily applied to future studies.

Rank aggregation aims to combine multiple rank lists into a single one, which has wide applications in recommender systems, link prediction, metasearch, proposal selection, and so on. Some existing studies have summarized and compared different rank aggregation algorithms. However, most of them cover only a few algorithms, the data used to test algorithms do not have a clear statistical property, and the metric used to quantify the aggregated results has certain limitations. Moreover, different algorithms all claim to be superior to existing ones when proposed, the baseline algorithms, the testing samples, and the application scenario are all different from case to case. Therefore, it is still unclear which algorithm is better for a particular task. Here we review nine rank aggregation algorithms and compare their performances in aggregating a small number of long rank lists. We assume an algorithm to generate different types of rank lists with known statistical properties and cause a more reliable metric to quantify the aggregation results. We find that despite the simplicity of heuristic algorithms, they work pretty well when the rank lists are full and have high similarities. In some cases, they can reach or even surpass the optimization-based algorithms in performance. The number of ties in the list will reduce the quality of the consensus rank and increase fluctuations. The quality of aggregated rank changes non-monotonically with the number of rank lists that need to be combined. Overall, the algorithm FAST outperforms all others in three different rank types, which can sufficiently complete the task of aggregating a small number of long rank lists.