The robustness of democratic consensus
Provides a theoretical framework for understanding when large-scale consensus systems are robust to individual agent influence, relevant to opinion dynamics and distributed algorithms.
The paper defines 'democratic consensus' as a property where each agent's influence on the final consensus value becomes negligible as the number of agents grows, and analyzes conditions for this property in linear consensus dynamics.
In linear models of consensus dynamics, the state of the various agents converges to a value which is a convex combination of the agents' initial states. We call it democratic if in the large scale limit (number of agents going to infinity) the vector of convex weights converges to 0 uniformly. Democracy is a relevant property which naturally shows up when we deal with opinion dynamic models and cooperative algorithms such as consensus over a network: it says that each agent's measure/opinion is going to play a negligeable role in the asymptotic behavior of the global system. It can be seen as a relaxation of average consensus, where all agents have exactly the same weight in the final value, which becomes negligible for a large number of agents.