Volume-based ranking method for a ranked voting system

초록

In a ranked voting system, candidates receive different votes in different ranking places. Many aggregation methods have been proposed to determine the ranking of the candidates competing for a limited number of positions. The most popular one is the weighted sum of votes that each candidate receives. The data envelopment analysis-based models also aggregate the submitted ranked votes into the final ranking of candidates by using the most favorable weights for each candidate. Most of such models, however, attempt to solve the problem with the discriminating factors (i.e., gaps between successive ranks) given specifically by zero or more restrictive constraints. This study presents a new ranking method for a ranked voting system that explicitly considers the unknown discriminating factors as they are. Specifically, we solve a dual of a dominance problem for a pair of candidates to effectively manage the unknown discriminating factors and then compute the volume of a set of the discriminating factors in favor of a candidate over another. A decision rule indicates that a candidate in a pair of candidates is preferred to another if the pair of candidates results in a larger volume than the reversed pair of candidates in that more discriminating factors necessarily yield a larger volume and thus more evidence in favor of a candidate over another exists. Therefore, the volume-based ranking method can be used to obtain the rank order of candidates in situations where any prior information on the discriminating factors is unavailable as is generally observed in real decision-making contexts.

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