Many-option collective decision making: discrete collective estimation in large decision spaces

Collective consensus forming in spatially distributed systems is a challenging task. In previous literature, multi-option consensus-forming scenarios, with the number of options being smaller or equal to the number of agents, have been well studied. However, many well-performing decision-making strategies on a few options suffer from scalability when the number of options increases, especially for many-option scenarios with significantly more options than agents. In this paper, we investigate the viabilities of discrete decision-making strategies with ranked voting (RV) and belief fusion (DBBS) decision mechanisms in many-option scenarios with large decision spaces compared to the number of agents. We test the investigated strategies on an expanded discrete collective estimation scenario where the decision space can be expanded using two factors: a higher number of environmental features and/or finer decision space discretization. We have used a continuous collective consensus forming strategy, linear consensus protocol (LCP), as a baseline. Our experimental results have shown that, although susceptible to environmental influences, discrete decision-making strategies can reliably outperform those of LCP in terms of error and convergence time at the tested sizes of decision space. We have also shown that the two factors that lead to the expansion of the decision space have different impacts on performances for both RV and DBBS strategies, due to differences in the correlations between the discrete options. When facing a higher number of features, both discrete strategies experience a smaller error and a significant increase in decision time, while a finer decision space discretization has a negative influence on all considered metrics.