A model of multi-agent consensus for vague and uncertain beliefs

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

Evidence Propagation and Consensus Formation in Noisy Environments

We study the effectiveness of consensus formation in multi-agent systems where there is both belief updating based on direct evidence and also belief combination between agents. In particular, we consider the scenario in which a population of agents collaborate on the best-of-n problem where the aim is to reach a consensus about which is the best (alternatively, true) state from amongst a set of states, each with a different quality value (or level of evidence). Agents' beliefs are represented within Dempster-Shafer theory by mass functions and we investigate the macro-level properties of four well-known belief combination operators for this multi-agent consensus formation problem: Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging operator. The convergence properties of the operators are considered and simulation experiments are conducted for different evidence rates and noise levels. Results show that a combination of updating on direct evidence and belief combination between agents results in better consensus to the best state than does evidence updating alone. We also find that in this framework the operators are robust to noise. Broadly, Yager's rule is shown to be the better operator under various parameter values, i.e. convergence to the best state, robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen