Heuristic for Diverse Kemeny Rank Aggregation based on Quantum Annealing

The Kemeny Rank Aggregation (KRA) problem is a well-studied problem in the field of Social Choice with a variety of applications in many different areas like databases and search engines. Intuitively, given a set of votes over a set of candidates, the problem asks to find an aggregated ranking of candidates that minimizes the overall dissatisfaction concerning the votes. Recently, a diverse version of KRA was considered which asks for a sufficiently diverse set of sufficiently good solutions. The framework of diversity of solutions is a young and thriving topic in the field of artificial intelligence. The main idea is to provide the user with not just one, but with a set of different solutions, enabling her to pick a sufficiently good solution that satisfies additional subjective criteria that are hard or impossible to model. In this work, we use a quantum annealer to solve the KRA problem and to compute a representative set of solutions. Quantum annealing is a meta search heuristic that does not only show promising runtime behavior on currently existing prototypes but also samples the solutions space in an inherently different way, making use of quantum effects. We describe how KRA instances can be solved by a quantum annealer and provide an implementation as well as experimental evaluations. As existing quantum annealers are still restricted in their number of qubits, we further implement two different data reduction rules that can split an instance into a set of smaller instances. In our evaluation, we compare classical heuristics that allow to sample multiple solutions such as simulated annealing and local search with quantum annealing performed on a physical quantum annealer. We compare runtime, quality of solution, and diversity of solutions, with and without applying preceding data reduction rules.