Data as voters: instance selection using approval-based multi-winner voting

We present a novel approach to the instance selection problem in machine learning (or data mining). Our approach is based on recent results on (proportional) representation in approval-based multi-winner elections. In our model, instances play a double role as voters and candidates. Each instance in the training set (acting as a voter) approves of the instances (playing the role of candidates) belonging to its local set (except itself), a concept already existing in the literature. We then select the election winners using a representative voting rule, and such winners are the data instances kept in the reduced training set.