Zealots Attack and the Revenge of the Commons: Quality vs Quantity in the Best-of-n

In this paper we study the effect of inflexible individuals with fixed opinions, or zealots, on the dynamics of the best-of-n collective decision making problem, using both the voter model and the majority rule decision mechanisms. We consider two options with different qualities, where the lower quality option is associated to a higher number of zealots. The aim is to study the trade-off between option quality and zealot quantity for two different scenarios: one in which all agents can modulate dissemination of their current opinion proportionally to the option quality, and one in which this capability is only possessed by the zealots. In both scenarios, our goal is to determine in which conditions consensus is more biased towards the high or low quality option, and to determine the indifference curve separating these two regimes. Using both numerical simulations and ordinary differential equation models, we find that: i) if all agents can modulate the dissemination time based on the option quality, then consensus can be driven to the high quality option when the number of zealots for the other option is not too high; ii) if only zealots can modulate the dissemination time based on the option quality, whil e all normal agents cannot distinguish the two options and cannot differentially disseminate, then consensus no longer depends on the quality and is driven to the low quality option by the zealots.