Study of Factors Influence on the Variability of Time for Consensus Building in Coalitions Based on Regular Markov Chains

Abstract

Draft standard is approved if and only if consensus of the technical committee for standardization (TC) is ensured before its approval by the standardization body at the national, regional and international level. Previously published works of authors dedicated to the construction of a mathematical model of time to build a consensus (number of negotiations) in terms of variation in the number of TC members and their level of authoritarianism. The present study is a continuation of these works for the case of the formation of coalitions in TC. The mathematical model is constructed to ensure consensus on the work of technical standardization committees in terms of coalitions, which are overcome during the negotiation process by concessions. This paper analyzes the factors, which influence the time for consensus building in this case: the value of the assignment and an index of the effect of the coalition. It is proved that the time to build a consensus signifi-cantly depends on the value of unilateral concessions coalition and weakly depends on the size of coalitions with a fixed number of TC members. Built regression model of dependence of the average number of approvals from the value of the assignment. It was revealed that even a small concession leads to the onset of consensus, increasing the size of the as-signment results (with other factors being equal) to a sharp decline in time before the consensus. It is shown that the as-signment of a larger coalition against small coalitions takes on average more time before building a consensus. The factors influencing the variability of the number of concessions were investigated. The change in the root-mean-square deviation (RMS) of the time to build a consensus varies nonlinearly from small concessions Y=10% to large Y=75%, regardless of the ratio of the number of members between coalitions. In the simulations, at concessions Y=10% there is the largest variation among the number of consensuses in the experiments. Concession of the authoritarian leader in group reduces the number of negotiations and increases the quality of consensus. The results obtained are of practical value for all structures where the emergence of coalitions entails the impossibility of consensual decision-making and requires consideration of different ways to build a consensual solution.

Keywords

• technical committee for standardization
• consensus
• coalition
• regular markov chains
• number of negotiations