# Evidence Propagation and Consensus Formation in Noisy Environments

## TL;DR

This paper investigates how multi-agent systems can effectively reach consensus on the best state despite noisy evidence, by analyzing belief combination operators within Dempster-Shafer theory through simulations.

## Contribution

It compares four belief combination operators in noisy environments, highlighting Yager's rule as the most effective for consensus and robustness.

## Key findings

- Yager's rule outperforms others in convergence and noise robustness
- Combining evidence updating with belief combination improves consensus accuracy
- Operators are generally robust to noise in the environment

## Abstract

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.