A Personalized Consensus Feedback Mechanism Based on Maximum Harmony Degree

This article proposes a framework of personalized feedback mechanism to help multiple inconsistent experts to reach consensus in group decision making by allowing to select different feedback parameters according to individual consensus degree. The general harmony degree (GHD) is defined to determine the before/after feedback difference between the original and revised opinions. It is proved that the GHD index is monotonically decreasing with respect to the feedback parameter, which means that higher parameter values will result in higher changes of opinions. An optimization model is built with the GHD as the objective function and the consensus thresholds as constraints, with the solution being personalized feedback advices to the inconsistent experts that keep a balance between consensus (group aim) and independence (individual aim). This approach is, therefore, more reasonable than the unpersonalized feedback mechanisms in which the inconsistent experts are forced to adopt feedback generated with only consensus target without considering the extent of the changes acceptable by individual experts. Furthermore, the following interesting theoretical results are also proved: 1) the personalized feedback mechanism guarantees that the increase of consensus level after feedback advices are implemented; 2) the GHD by the personalized feedback mechanism is higher than that of the unpersonalized one; and 3) the personalized feedback mechanism generalizes the unpersonalized one as it is proved the latter is a particular type of the former. Finally, a numerical example is provided to model the feedback process and to corroborates these results when comparing both feedback mechanism approaches.