Clustering alternatives in preference-approvals via novel pseudometrics

Abstract

Preference-approval structures combine preference rankings and approval voting for declaring opinions over a set of alternatives. In this paper, we propose a new procedure for clustering alternatives in order to reduce the complexity of the preference-approval space and provide a more accessible interpretation of data. To that end, we present a new family of pseudometrics on the set of alternatives that take into account voters’ preferences via preference-approvals. To obtain clusters, we use the Ranked k-medoids (RKM) partitioning algorithm, which takes as input the similarities between pairs of alternatives based on the proposed pseudometrics. Finally, using non-metric multidimensional scaling, clusters are represented in 2-dimensional space.