On condition of reaching a high level of consensus when new decision makers join

Abstract

Purpose – The consensus opinion helps with the achievement of fairness of the decision process, especially when the new decision makers (DMs) are added into the group decision making (GDM). This paper aims to show by constructing consensus models that when some conditions are met, the consensus level does not decrease even when new DMs are invited to join the GDM (new opinions are added to the GDM). Design/methodology/approach – This paper first constructs a deviation which is the difference between each two individual opinions. The smaller these differences are, the higher consensus degree (level) of the group. Then, a consensus optimization model based on individual differences (IDCO) is constructed by minimizing the aggregated deviations. Lastly, based on the optimization model, the condition of reaching a high level of consensus when new DMs are added into the GDM is discussed. Findings – The discussion on the properties of the IDCO indicates that once the consensus with all DMs reaching an acceptable level, the consensus deviation degree decreases as the number of DMs increases when certain conditions are met, and the consensus level does not decrease even when new DMs join the GDM. Originality/value – Practically, high-level consensus needs to be reached no matter how difficult it is when the new opinions are added into the GDM. To see how this end could be achieved, this paper takes the fuzzy preference relations as particular instances to investigate the conditions of consensus under which new DMs (opinions) are added into the GDM. The rather holistic analysis leads us to such a conclusion that the authors can replace this particular kind of preference, as used in the discussion, in many other cases by, for instance, multiplicative preference relation, linguistic preference relation, etc.