A Study on Effective Total Ranking Models for Preferential Voting Problems

A ranked voting system is one of the most conventional methods to make group decisions. In this system, each voter selects a subset of candidates and ranks them from most to least preferred. Since the pioneering work of Cook and Kress (1990)’ DEA-based voting model, numerous variants addressing the ranked voting problems have been presented in the literature. Among them, two improved DEA-based voting models were presented to determine the weights associated with rank positions, arguing that the proposed models are simple, and each of them can lead to a stable full ranking for all the candidates considered. Despite the contribution to the DEA-based voting models, some drawbacks are revealed in the theories associated with the model and thus this study provides a more rigorous solution based on algebraic methods. Furthermore, we stress that the findings while addressing those drawbacks can also be applied to similar DEA-based voting problems that have other types of constraints to make gaps between rank positions. Finally, we present a closed form solution of the second model in line with the theories developed in association with the first model. It means that the weights associated with rank positions as well as the full ranking of candidates can be immediately determined with no need for the linear programming software as was done in the first model.