Dynamics of majority rule with differential latencies

Spontaneous opinion swings in the voter model with latency

The cognitive process of opinion formation is often characterized by stubbornness or resistance of agents to changes of opinion. To capture this feature we introduce a constant latency time in the standard voter model of opinion dynamics: after switching opinion, an agent must keep it for a while. This seemingly simple modification drastically changes the stochastic diffusive behavior of the original model, leading to deterministic dynamical oscillations in the average opinion of the agents. We explain the origin of the oscillations and develop a mathematical formulation of the dynamics that is confirmed by extensive numerical simulations. We further characterize the rich phase space of the model and its asymptotic behavior. Our work offers insights into understanding and modeling the phenomenon of opinion swings, often observed in diverse social contexts.

Speed-accuracy trade-offs in best-of-n collective decision making through heterogeneous mean-field modeling

To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best option among a set of alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it! Thanks to their mathematical tractability, simple models like the voter model and the local majority rule model have proven useful to describe the dynamics of such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbors in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, by the need to reduce the cognitive load. Our analysis is grounded on the introduction of a model that generalizes the two existing models (local majority rule and voter model), showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show the presence of another speed-accuracy trade-off regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy.

The k -Unanimity Rule for Self-Organized Decision-Making in Swarms of Robots

In this paper, we propose a collective decision-making method for swarms of robots. The method enables a robot swarm to select, from a set of possible actions, the one that has the fastest mean execution time. By means of positive feedback the method achieves consensus on the fastest action. The novelty of our method is that it allows robots to collectively find consensus on the fastest action without measuring explicitly the execution times of all available actions. We study two analytical models of the decision-making method in order to understand the dynamics of the consensus formation process. Moreover, we verify the applicability of the method in a real swarm robotics scenario. To this end, we conduct three sets of experiments that show that a robotic swarm can collectively select the shortest of two paths. Finally, we use a Monte Carlo simulation model to study and predict the influence of different parameters on the method.