Consensus formation is investigated for multi-agent systems in which agents' beliefs are both vague and uncertain. Vagueness is represented by a third truth state meaning borderline. This is combined with a probabilistic model of uncertainty. A belief combination operator is then proposed, which exploits borderline truth values to enable agents with conflicting beliefs to reach a compromise. A number of simulation experiments are carried out, in which agents apply this operator in pairwise interactions, under the bounded confidence restriction that the two agents' beliefs must be sufficiently consistent with each other before agreement can be reached. As well as studying the consensus operator in isolation, we also investigate scenarios in which agents are influenced either directly or indirectly by the state of the world. For the former, we conduct simulations that combine consensus formation with belief updating based on evidence. For the latter, we investigate the effect of assuming that the closer an agent's beliefs are to the truth the more visible they are in the consensus building process. In all cases, applying the consensus operators results in the population converging to a single shared belief that is both crisp and certain. Furthermore, simulations that combine consensus formation with evidential updating converge more quickly to a shared opinion, which is closer to the actual state of the world than those in which beliefs are only changed as a result of directly receiving new evidence. Finally, if agent interactions are guided by belief quality measured as similarity to the true state of the world, then applying the consensus operator alone results in the population converging to a high-quality shared belief.
The idea of bounded confidence @cite_9 @cite_2 has been proposed as a mechanism by which agents limit their interactions with others, so that they only combine their beliefs with individuals holding opinions which are sufficiently similar to their current view. A version of bounded confidence is also used in our proposed model, where each agent measures the relative inconsistency of their beliefs with those of others, and is then only willing to combine beliefs with agents whose inconsistency measure is below a certain threshold.
@cite_9 @cite_2
2159918425 1582135188 1517494768 1965649844
Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines such as physics, mathematics, computer science, social psychology and philosophy. In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte Carlo style, but they can also be reformulated on the agent's density in the opinion space in a master equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds o... Abstract: We model opinion dynamics in populations of agents with continuous opinion and uncertainty. The opinions and uncertainties are modified by random pair interactions. We propose a new model of interactions, called relative agreement model, which is a variant of the previously discussed bounded confidence. In this model, uncertainty as well as opinion can be modified by interactions. We introduce extremist agents by attributing a much lower uncertainty (and thus higher persuasion) to a small proportion of agents at the extremes of the opinion distribution. We study the evolution of the opinion distribution submitted to the relative agreement model. Depending upon the choice of parameters, the extremists can have a very local influence or attract the whole population. We propose a qualitative analysis of the convergence process based on a local field notion. The genericity of the observed results is tested on several variants of the bounded confidence model. This paper studies asymptotic consensus in systems in which agents do not necessarily have self-confidence, i.e., may disregard their own value during execution of the update rule. We show that the prevalent hypothesis of self-confidence in many convergence results can be replaced by the existence of aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually store information about an agent's value distributedly in the network. Our results are applicable to systems with message delays and memory loss. We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.