Mean-Median Compromise Method: A Novel Deepest Voting Function Balancing Range Voting and Majority Judgment - Ruffin-Benoît M. Ngoie; Selain K. Kasereka; Jean-Aimé B. Sakulu; Kyandoghere Kyamakya (Mathematics, 2024)
A logical presentation of the Mean-Median Compromise Method (MMCM) is provided in this paper. The objective is to show that the method is a generalization of majority judgment, where each tie-break step is <semantics>Lp</semantics> deepest voting. Therefore, in its tie-breaking procedures, the proposed method returns scores that range from the median to the mean. Among the established characteristics that it satisfies are universality, neutrality, independence of irrelevant alternatives, unanimity, and monotonicity. Additionally covered are robustness, reaching consensus, controlling extremes, responding to single-peakedness, and the impact of outliers. Through computer simulations, it is shown that the MMCM score does not vary by more than 12% even for up to 50% of strategic voters, ensuring the method’s robustness. The 1976 Paris wine taste along with the French presidential poll organized by OpinionWay in 2012 were well-known and highly regarded situations in the area of social choice to which the MMCM was used. The outcomes of MMCM have shown remarkable consistency. On the basis of the democratic standards that are most frequently discussed in the literature, other comparisons were performed. With 19 of the 25 criteria satisfied, the MMCM is in the top ranking. Supporting theorems have shown that MMCM does not necessarily require an absolute majority to pass an opinion for which a minority expresses a strong preference while the majority is only marginally opposed.