Score Aggregation via Spectral Method

Abstract

The score aggregation problem is to find an aggregate scoring over all candidates given individual scores provided by different agents. This is a fundamental problem with a broad range of applications in social choice and many other areas. The simple and commonly used method is to sum up all scores of each candidate, which is called the sum-up method. In this paper, we give good algebraic and geometric explanations for score aggregation, and develop a spectral method for it. If we view the original scores as `noise data', our method can find an `optimal' aggregate scoring by minimizing the `noise information'. We also suggest a signal-to-noise indicator to evaluate the validity of the aggregation or the consistency of the agents.