Related papers: 3-Majority and 2-Choices with Many Opinions
We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional space at a constant speed in a direction that is randomly assigned initially. Then, at…
When opinions, behaviors or ideas diffuse within a population, some are invariably stickier than others. The stickier the opinion, behavior or idea, the greater is an individual's inertia to replace it with an alternative. Here we study the…
We study the evolution of majority dynamics on Erd\H{o}s-R\'enyi $G(n,p)$ random graphs. In this process, each vertex of a graph is assigned one of two initial states. Subsequently, on every day, each vertex simultaneously updates its state…
Let $G = (V,E)$ be a connected directed graph on $n$ vertices. Assign values from the set $\{1,2,\dots,n\}$ to the vertices of $G$ and update the values according to the following rule: uniformly at random choose a vertex and update its…
Our goal is to find a necessary and sufficient condition on the consensus over a random network, generated by i.i.d. stochastic matrices. We show that the consensus problem in three different convergence modes (almost surely, in…
This article is concerned with a general class of stochastic spatial models for the dynamics of opinions. Like in the voter model, individuals are located on the vertex set of a connected graph and update their opinion at a constant rate…
We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $\pm 1$, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the…
We consider a class of opinion dynamics on networks where at each time-step, each node in the network disregards the opinions of a certain number of its most extreme neighbors and updates its own opinion as a weighted average of the…
In this paper, and inspired by the recent discrete-time model in [1,2], we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The…
We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is "correct" with probability $\frac{1}{2}+\delta$ for some $\delta…
People's opinions evolve over time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but…
In this modification of the Sznajd consensus model on the square lattice, two people of arbitrary distance who agree in their opinions convince their nearest neighbours of this opinion. Similarly to the mean field theory of Slanina and…
Consider a graph $G$, representing a social network. Assume that initially each node is colored either black or white, which corresponds to a positive or negative opinion regarding a consumer product or a technological innovation. In the…
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…
Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…
We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a…
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation…
This paper gives lower bounds for the probability of consensus for two spatially explicit stochastic opinion models. Both processes are characterized by two finite connected graphs, that we call respectively the spatial graph and the…
The voter model is an archetypal stochastic process that represents opinion dynamics. In each update, one agent is chosen uniformly at random. The selected agent then copies the current opinion of a randomly selected neighbour. We…
We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs. For instance, it is known how to maintain a 1/2-approximate matching in $\log^{O(1)} n$…