Consensus decision models for preferential voting with abstentions

Proper use of the data envelopment analysis (DEA) for aggregating preferential rankings helps improve efficiency of a voting system. It has been observed that many recent elections often have low turnouts, a large number of abstentions and invalid ballots. If these voters can be influenced to cast their votes for or against a candidate, it is understandable that the voting result can be quite different. The purpose of this research is to incorporate abstentions into preferential voting models. To this end, we first introduce a preferential voting DEA model with abstentions, in which the raw votes are expressed as interval values and the width of the interval characterizes the number of uncertain votes, the objective function is to maximize a candidate's weighted voting score, and the constraints put restrictions on the place weights to ensure a proper importance order of different places. Secondly, given the fact that opinion leaders often employ different means such as social media and advertisement to influence voters in real-world elections, we explicitly incorporate these opinion leaders/brokers as a moderator into a preferential voting model with abstentions and introduce a moderator-involved-consensus preferential voting (MICPV) model. This model aims to capture the moderator's influences on the uncertain voters from a consensus perspective. The optimal allocation of all uncertain votes allows the moderator to maximize his/her influence over the voters to achieve the minimum deviation between his/her expected and the aggregate scores of the candidates. At the optimality, for those candidates where a complete consensus is achievable, the model identifies the optimal allocation scheme. We also analyze the economic significance of the MICPV model.