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.

偏好批准结构结合了偏好排名和批准投票，以表达对一组替代方案的意见。在本文中，我们提出了一种对备选方案进行聚类的新程序，以降低偏好批准空间的复杂性并提供更易于理解的数据解释。为此，我们提出了一系列关于替代方案的新伪计量学，这些替代方案通过偏好批准考虑了选民的偏好。为了获得聚类，我们使用排名k中心点 (RKM) 分区算法，该算法将基于所提出的伪度量的备选方案对之间的相似性作为输入。最后，使用非度量多维缩放，在二维空间中表示簇。