Related papers: Asynchronous 3-Majority Dynamics with Many Opinion…
We study a distributed consensus problem on a complete communication network of $n$ vertices, each holding one of two opinions. The vertices communicate in rounds, possibly in the presence of adversarial noise, and exchange information…
Majority dynamics is a process on a simple, undirected graph $G$ with an initial Red/Blue color for every vertex of $G$. Each day, each vertex updates its color following the majority among its neighbors, using its previous color for…
We study majority dynamics on the binomial random graph $G(n,p)$ with $p = d/n$ and $d > \lambda n^{1/2}$, for some large $\lambda>0$. In this process, each vertex has a state in $\{-1,+1 \}$ and at each round every vertex adopts the state…
Given a graph $G$ and some initial labelling $\sigma : V(G) \to \{Red, Blue\}$ of its vertices, the \textit{majority dynamics model} is the deterministic process where at each stage, every vertex simultaneously replaces its label with the…
We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on…
We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multi-way interactions. We compare this dynamics with that on appropriate projections of this higher-order network representation…
We analyze the convergence of the $k$-opinion Undecided State Dynamics (USD) in the population protocol model. For $k$=2 opinions it is well known that the USD reaches consensus with high probability within $O(n \log n)$ interactions.…
Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnel, Tamuz and Tan…
This paper is about a new model of opinion dynamics with opinion-dependent connectivity. We assume that agents update their opinions asynchronously and that each agent's new opinion depends on the opinions of the $k$ agents that are closest…
We generalize a binary majority-vote model on adaptive networks to its plurality-vote counterpart and analyze the time scale to consensus when voters are given more than two options. When opinions are uniformly distributed in the population…
The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase…
Consider n individuals who, by popular vote, choose among q >= 2 alternatives, one of which is "better" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better…
We study the voter dynamics model on heterogeneous graphs. We exploit the non-conservation of the magnetization to characterize how consensus is reached on networks with different connectivity patterns. For a network of N sites with an…
This paper is concerned with the probability of consensus in a multivariate, spatially explicit version of the Hegselmann-Krause model for the dynamics of opinions. Individuals are located on the vertices of a finite connected graph…
We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node…
We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the…
We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…
We generalize a binary majority-vote model on adaptive networks to a plurality-vote counterpart. When opinions are uniformly distributed in the population of voters in the initial state, it is found that having more available opinions in…
Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph…
We consider a system in which a group of agents represented by the vertices of a graph synchronously update their opinion based on that of their neighbours. If each agent adopts a positive opinion if and only if that opinion is sufficiently…