Robot swarm democracy: the importance of informed individuals against zealots

In this paper we study a generalized case of best-of-n model, which considers three kind of agents: zealots, individuals who remain stubborn and do not change their opinion; informed agents, individuals that can change their opinion, are able to assess the quality of the different options; and uninformed agents, individuals that can change their opinion but are not able to assess the quality of the different opinions. We study the consensus in different regimes: we vary the quality of the options, the percentage of zealots and the percentage of informed versus uninformed agents. We also consider two decision mechanisms: the voter and majority rule. We study this problem using numerical simulations and mathematical models, and we validate our findings on physical kilobot experiments. We find that (1) if the number of zealots for the lowest quality option is not too high, the decision-making process is driven toward the highest quality option; (2) this effect can be improved increasing the number of informed agents that can counteract the effect of adverse zealots; (3) when the two options have very similar qualities, in order to keep high consensus to the best quality it is necessary to have higher proportions of informed agents.