Time to Consensus in International Negotiations

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Contemporary international relations, anchored in the principles of multipolarity, frequently employ consensus-based decision-making, which prioritizes respect for all negotiating parties and ensures that the views of all participants are considered equally. While consensus remains a core mechanism for many international organizations, such as the World Trade Organization (WTO), it has increasingly come under criticism for its inefficiency and substantial time requirements. This highlights the importance of examining the factors that influence the time needed to reach consensus. Utilizing formal mathematical modeling based on a modified DeGroot model, this article explores how variables such as the size of the negotiating group, the level of authoritativeness, dominance dynamics within the group, and coalition formation affect the time required to achieve consensus. The findings indicate that an increase in group size, on its own, results in only a minor increase in the time needed to reach consensus, becoming a significant factor only when paired with high levels of authoritativeness among the participants. Conversely, the presence of a highly authoritative member within a negotiating group significantly prolongs decision-making time, even in smaller groups, and the formation of coalitions (e.g., due to multiple highly authoritative members) can make reaching consensus impossible. The "consensus minus k" rule, intended to break deadlocks, is found to be ineffective for international organizations with numerous participants and divergent interests. In hierarchical structures, consensus is typically achieved through preliminary negotiations within subgroups, which further prolongs the consensusbuilding process.