A universal voting system based on the Potential Method

Abstract

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 to obtain a value function (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, each criterion or decision maker is represented by its preference graph. A multigraph obtained by joining these graphs aggregates the individual preferences and generates the group potential. Moreover, the influence (weight) of each criterion or decision maker on the group potential may be adjusted. In this article the 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. As an illustration of the PM in the voting context we have chosen the Eurovision Song Contest and the analysis of the cookie-type ballots where the voters allocate a certain number of points (cookies) to the candidates.