# Consensus dynamics

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Consensus_dynamics
> Markdown URL: https://mediated.wiki/source/Consensus_dynamics.md
> Source: https://en.wikipedia.org/wiki/Consensus_dynamics
> Source revision: 1300000049
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

How a group of agents can reach a common decision

**Consensus dynamics**, also known as **agreement dynamics**, is an area of research at the intersection of [systems theory](/source/Systems_theory) and [graph theory](/source/Graph_theory). It studies how a group of agents—such as robots, sensors, or decision-makers—interacting over a network can reach a common decision or estimate through local rules and information exchange. This is known as the consensus problem in [multi-agent systems](/source/Multi-agent_system), where the goal is to ensure that all agents eventually agree on a certain quantity, despite starting with potentially different initial values.

Consensus dynamics has applications in areas such as [physiological systems](/source/Physiological_system), [gene regulatory networks](/source/Gene_regulatory_network), [large-scale energy systems](/source/Power_grid), and coordinated control of autonomous vehicle fleets on land, in the air, or in space. The behavior of these systems is typically modeled using an unforced [dynamical system](/source/Dynamical_system) governed by the network's interconnection topology and the agents' initial conditions. The **consensus protocol**, or **agreement protocol**, defines the rules of interaction that lead to convergence.

Related coordination problems include the [rendezvous problem](/source/Rendezvous_problem), [synchronization](/source/Synchronization), [flocking](/source/Flocking_(behavior)), and [formation control](/source/Formation_control). These often rely on similar mathematical foundations and are studied under the broader umbrella of **cooperative control**. One computational approach to solving these problems is [distributed constraint reasoning](/source/Distributed_constraint_reasoning). Consensus models are also used in social and philosophical domains to analyze how groups reach agreement through debate or deliberation. For example, simulations can evaluate whether introducing a new argument shifts the outcome of a debate by providing an additional truth value.[1]

## See also

- [Consensus (computer science)](/source/Consensus_(computer_science))

- [Cooperative multitasking](/source/Cooperative_multitasking)

## References

1. **[^](#cite_ref-Betz2012_1-0)** Gregor Betz (15 August 2012). [*Debate Dynamics: How Controversy Improves Our Beliefs*](https://books.google.com/books?id=v4bV5a7yE4wC&pg=PA189). Springer Science & Business Media. pp. 189–. [ISBN](/source/ISBN_(identifier)) [978-94-007-4599-5](https://en.wikipedia.org/wiki/Special:BookSources/978-94-007-4599-5).

- Ghapani, S.; Mei, J.; Ren, W.; Song, Y. (2016), "Fully distributed flocking with a moving leader for lagrange networks with parametric uncertainties", *Automatica*, 67–76, [doi:10.1016/j.automatica.2016.01.004](https://doi.org/10.1016/j.automatica.2016.01.004)

- Shamma, Jeff S. (2008). *Cooperative Control of Distributed Multi-Agent Systems*. Wiley-Interscience. [ISBN](/source/ISBN_(identifier)) [978-0-470-06031-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-06031-5).

---
Adapted from the Wikipedia article [Consensus dynamics](https://en.wikipedia.org/wiki/Consensus_dynamics) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Consensus_dynamics?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.