Pairwise comparison of various objects (alternatives) is common in many procedures related to decision making. Potential Method (PM) uses a (weighted) preference graph as the basic structure generated by such comparisons. This graph implies a value function (called potential) on the set of alternatives. The potential is calculated as a solution of a system of equations involving the Laplacian matrix of the preference graph. In multiple-criteria decision analysis or group decision making (i.e., voting systems), each criterion or decision maker is represented by a preference graph. A multigraph obtained by joining these graphs is used for preference aggregation, generating the group potential. We can set arbitrary weights to adjust the influence of each criterion or decision maker on the group potential. Aggregation of preference graphs is applied to voting systems. Many different forms of voting ballots can generate preference graphs, which gives us a universal (ballot-independent) voting system. Another application is a cluster analysis of the group based on the members’ preferences, where a hierarchical or partitional clustering of their (multiple) preference graphs should be performed. In this context, the multigraph-based aggregation is used to define the center of the cluster or the distance between two clusters. As an illustration, we have applied the described voting system, as well as the cluster analysis, to the voting data from the Eurovision Song Contest.