Study of Decision-making Issues in Social Groups Based on Modelling of Incomplete Consensus

In many social groups, for example, in European eco-settlements, social movements (occupy), international organizations (WTO, OSCE, IPCC, etc.), decision-making is based on the consensus of the group members. Instead of voting, when the majority wins over the minority, consensus allows finding a solution that each member of the group supports or, at least, considers acceptable. This approach ensures that all the opinions of the group members, their ideas and needs will be taken into account. At the same time, reaching a consensus requires considerable time, since it is necessary to come to an agreement within the group, regardless of its size. It was shown that in some situations the number of iterations (agreements, negotiations) is very significant. Moreover, in the decision-making process, there is always a risk of blocking a decision by a minority in the group, which not only prolongs the decision-making time but even makes it impossible. As a rule, such a minority is presented by one or two odious people. Such a member of the group tries to dominate the discussion, always stands by his/her opinion, ignoring the position of the others. This leads to a protraction in the decision-making process, on the one hand, and a deterioration in the quality of consensus, on the other, since only the opinion of the dominant part of the group would be taken into account.In order to overcome this problem, it was proposed to make a decision based on the principle of “Consensus Minus One” or “Consensus Minus Two”, that is, not to take into account the opinion of one or two odious members of the group. For example, in climate researches, where many scientific disciplines are involved, a complete consensus is almost impossible. Based on the simulation of consensus using the Markov chain model, the article studies the question of how much the decision-making time is reduced when using the “Consensus Minus One” and “Consensus Minus Two” rules, if the position of the dominant members of the group is not taken into account. As it appears from the findings obtained, this paper can be in general summarized by saying that the rule of thumb applied for making a decision pursuant to the incomplete consensus principle has a solid mathematical background. The simulation results showed that its use can reduce the time required to reach a consensus to 97%, which is crucial for practice. The average number of agreements hyperbolically depends on the average authoritarianism of the group members (excluding the autocratic members), which means that the negotiation process can be protracted at high values of the above-mentioned average authoritarianism.