|This is a supplementary document for the Special Issue of Swarm Intelligence 2020 Paper titled Robot swarm democracy: the importance of informed individuals against zealots
Table of Contents
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
- if the number of zealots for the lowest quality option is not too high, the decision making process is driven towards the highest quality option;
- this effect can be improved increasing the number of informed agents that can counteract the effect of adverse zealots;
- 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.
Keywords: Collective Decision Making, Swarm Intelligence, Swarm Robotics, Stubborn agents
Results with Software Simulation
A population of 100 agents is simulated, where the percentage of zealot A (here represented with red color) is 22.5%, while the percentage of zealots B (here represented with blue color) is 1.25%. Red color represents opinion A, while blue color represents opinion blue. Usual bees are represented by circles, while zealots have star shape. The two options have quality ratio is 1.5. The voting method is the majority rule (k=3). In the first video, all normal agents are uninformed. In the second video, all normal agents are informed.
Results with Physical Robots
The experiments include 40 kilobots, where the zealot A (here represented with pink color) proportion is 0.225, while the zealot B (here represented with light blue color) proportion is 0.025. The voting method is the majority rule (k=3). In the first and second videos, all normal agents (represented with red and blue color) are uninformed with the quality ratio 1.5 and 1. In the third and fourth videos, all normal agents are informed with the quality ratio 1.5 and 1.
Heatmap showing the proportion of agents with opinion A in the case where half of the agents are informed and half are uniformed (phi=0.5, voter model)