Listen to Your Neighbors: How (Not) to Reach a Consensus

Abstract

We study the following rather generic communication\slash coordination\slash computation problem: In a finite network of agents, each initially having one of the two possible states, can the majority initial state be computed and agreed upon by means of local computation only? We study an iterative synchronous application of the local majority rule and describe the architecture of networks that are always capable of reaching the consensus on the majority initial state of its agents. In particular, we show that, for any truly local network of agents, there are instances in which the network is not capable of reaching such a consensus. Thus, every truly local computational approach that requires reaching a consensus is not failure-free.