Consensual Affine Transformations for Partial Valuation Aggregation

We consider the task of aggregating scores provided by experts that each have scored only a subset of all objects to be rated. Since experts only see a subset of all objects, they lack global information on the overall quality of all objects, as well as the global range in quality. Inherently, the only reliable information we get from experts is therefore the relative scores over the objects that they have scored each. We propose several variants of a new aggregation framework that takes this into account by computing consensual affine transformations of each expert's scores to reach a globally balanced view. Numerical comparisons with other aggregation methods, such as rank-based methods, Kemeny Young scoring, and a maximum likelihood estimator, show that the new method gives significantly better results in practice. Moreover, the computation is practically affordable and scales well even to larger numbers of experts and objects.