A Dynamic Programming Approach to the Rank Aggregation Problem

Rank aggregation is an essential approach for aggregating the preferences of multiple agents. One rank aggregation rule of particular interest is the Kemeny rule, which maximises the number of pairwise agreements between the final ranking and the existing rankings, and has an important interpretation as a maximum likelihood estimator. However, Kemeny rankings are NP-hard to compute. This has resulted in the development of various algorithms for computing Kemeny rankings. Fortunately, NP-hardness may not reflect the difficulty of solving problems that arise in practice. As a result, we aim to demonstrate that the Kemeny consensus can be computed efficiently when aggregating different rankings in real case. In this paper, we describe a dynamic programming model for aggregating university rankings. We also provide details on the implementation of the model. Finally, we present results obtained from an experimental comparison of different models based on real world and randomly generated problem instances, and show that the dynamic programming approach has comparable efficiency as other approaches.