  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. The approval set
of each instance in the training set (acting as a voter) is defined from the
concept of local set, which already exists in the literature. We then select
the election winners by using a representative voting rule, and such winners
are the data instances kept in the reduced training set. Our experiments show
that, for KNN, the rule Simple 2-EJR (a variant of the Simple EJR voting rule
that satisfies 2-EJR) outperforms all the state-of-the-art algorithms and all
the baselines that we consider in this paper in terms of accuracy vs reduction.
For SVMs, we have obtained slight increases in the average accuracy by using
several voting rules that satisfy EJR or PJR compared to the results obtained
with the original datasets.
