Agreement algorithm using the trial and error method at the macrolevel

The best-of-n problem (Valentini et al. in Front Robot AI 4(9):1–18, 2017) is one of the decision-making problems in which many robots (agents) select the best option among a set of n alternatives and are focused on the field of Swarm Robotics. Almost all of the previous studies focused on binary decision-making scenarios (\(n = 2\)) and could not be applied without any change in the case of \(n> 2\). It is necessary to satisfy constraints on the number of robots N, or the time required for reaching the best option is abruptly increased. Therefore, it is required to construct a method that can deal with \(n> 2\). In this paper, we propose an algorithm (BRT model, bias and rising threshold model) in which the time and the possibility of reaching agreement are not dependent on the number of robots N even when \(n> 2\). By computer experiments, our claims are verified within the tested parameter ranges.