Effect of higher-order interactions on noisy majority-rule dynamics with random group sizes
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Research Center for Quantum Physics, BRIN（BRIN量子物理研究中心）；Department of Physics, POSTECH（浦项工科大学物理系）；Department of Physics, Korea University（韩国大学物理系）；Department of Physics, Universitas Gadjah Mada（加查马达大学物理系）
Roni Muslim, Jong-Min Park, Jihye Kim, Rinto Anugraha NQZ
We study opinion dynamics with higher-order interactions, motivated by the fact that social influence often takes place in groups rather than only through pairwise contacts. We introduce a noisy majority-rule model on annealed hypergraphs with heterogeneous group sizes and investigate how the distribution of interaction sizes affects collective ordering and relaxation. Using analytical theory and Monte Carlo simulations, we show that group-size heterogeneity strongly shapes both the transition between ordered and mixed states and the associated time scales. In particular, broader and heavier-tailed distributions make ordering more robust by enhancing the effect of rare large-group events. They also modify the finite-size scaling of relaxation, producing a crossover from the standard logarithmic behavior to faster ordering in sufficiently broad ensembles. In the pure majority-rule limit, we further show that the exit probability near coexistence obeys a universal error-function scaling form controlled by a single structural parameter. Our results demonstrate that the full distribution of group sizes is a key determinant of nonequilibrium ordering in higher-order opinion dynamics.
We study how groups reach consensus by varying communication network structure and individual incentives. In 342 networks of seven individuals, single opinionated "leaders" can drive decision outcomes, but do not accelerate consensus formation, whereas conflicting opinions slow consensus. While networks with more links reach consensus faster, this advantage disappears under conflict. Unopinionated individuals make choices consistent with a local majority rule combined with "inertia" favouring their previous choice, while opinionated individuals favour their preferred option but yield under hig…
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 majority opinion if all group members belong to the same class; if not, majority rule is applied with probability $ε$. Consensus is achieved in a time that scales logarithmically with population size if $ε\geq ε_c=\frac{1}{9}$. For $ε<ε_c$, the population can get trapped in a polarized state, with one class preferring the $+1$ state and the other preferring $-…
The equilibrium states associated with the local majority-rule are divided into three classes, the states of system-wide coordination, the trapped states, and the states of period-2. The effect of clustering coefficient on the occurrence probability of the states of three classes is analyzed numerically for Watts-Strogatz and scale-free networks. We further study the effect of clustering coefficient on the robustness for the states of each class by proposing a stochastic local majority-rule. The states of period-2 are found to be easy to break up, and the trapped states are most robust among t…
We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.
In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups that, at each evolution step, gather to reach agreement. When the group size distribution has a finite mean value, the previously known logarithmic dependence on the population size holds. On the other hand, when the mean group size diverges, the consensus time and the population size are related through a power law. Numerical simulations validate this semi-qu…
In this paper, we study how an agent's belief is affected by her neighbors in a social network. We first introduce a general framework, where every agent has an initial belief on a statement, and updates her belief according to her and her neighbors' current beliefs under some belief evolution functions, which, arguably, should satisfy some basic properties. Then, we focus on the majority rule belief evolution function, that is, an agent will (dis)believe the statement iff more than half of her neighbors (dis)believe it. We consider some fundamental issues about majority rule belief evolution,…
A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule, and investigate the possibility to represent and analyse the system by means of hypergraphs. We explore the formation of consensus and restrict our attention to interaction groups of size $3$, in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or degree heterog…
Interaction size and dissent tolerance in majority-rule dynamics with collective reversal
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Research Center for Quantum Physics, National Research and Innovation Agency (BRIN)（国家研究与创新署（BRIN）量子物理研究中心）；Department of Physics, Gadjah Mada University（加札马达大学物理系）
We investigate the dynamics of the majority-rule opinion formation model when voters experience differential latencies. With this extension, voters that just adopted an opinion go into a latent state during which they are excluded from the opinion formation process. The duration of the latent state depends on the opinion adopted by the voter. The net result is a bias towards consensus on the opinion that is associated with the shorter latency. We determine the exit probability and time to consensus for systems of $N$ voters. Additionally, we derive an asymptotic characterisation of the time to…
We study the effects of free will and massive opinion of multi-agents in a majority rule model wherein the competition of the two types of opinions is taken into account. To address this issue, we consider two specific models (model I and model II) involving different opinion-updating dynamics. During the opinion-updating process, the agents either interact with their neighbors under a majority rule with probability $1-q$, or make their own decisions with free will (model I) or according to the massive opinion (model II) with probability $q$. We investigate the difference of the average number…
Crowdsourcing is a mechanism by means of which groups of people are able to execute a task by sharing ideas, efforts and resources. Thanks to the online technologies, crowdsourcing has become in the last decade an even more utilized process in different and diverse fields. An instance of such process is the so-called "label aggregation problem": in practice, it is the evaluation of an item by groups of agents, where each agent gives its own judgment of it. Starting from the individual evaluations of their members, how can the groups give their global assessment? In this work, by means of a gam…
Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have …
In this work we study opinion formation in a population participating of a public debate with two distinct choices. We considered three distinct mechanisms of social interactions and individuals' behavior: conformity, nonconformity and inflexibility. The conformity is ruled by the majority-rule dynamics, whereas the nonconformity is introduced in the population as an independent behavior, implying the failure to attempted group influence. Finally, the inflexible agents are introduced in the population with a given density. These individuals present a singular behavior, in a way that their stub…
In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the…
Majority-vote model is a much-studied model for social opinion dynamics of two competing opinions. With the recent appreciation that our social network comprises a variety of different layers forming a multiplex network, a natural question arises on how such multiplex interactions affect the social opinion dynamics and consensus formation. Here, the majority-vote model will be studied on multiplex networks to understand the effect of multiplexity on opinion dynamics. We will discuss how global consensus is reached by different types of voters: AND- and OR-rule voters on multiplex-network and v…
We present numerical results on a complex dynamical model for the aggregation of many individual rankings of S alternatives by the pairwise majority rule under a deliberative scenario. Agents are assumed to interact when the Kemeny distance between their rankings is smaller than a range R. The main object of interest is the probability that the aggregate (social) ranking is transitive as a function of the interaction range. This quantity is known to decay fast as S increases in the non-interacting case. Here we find that when S>4 such a probability attains a sharp maximum when the interaction …
We study a network model that couples the dynamics of link states with the evolution of the network topology. The state of each link, either A or B, is updated according to the majority rule or zero-temperature Glauber dynamics, in which links adopt the state of the majority of their neighboring links in the network. Additionally, a link that is in a local minority is rewired to a randomly chosen node. While large systems evolving under the majority rule alone always fall into disordered topological traps composed by frustrated links, any amount of rewiring is able to drive the network to comp…
We study the effect of probabilistic distortions to the local majority rules used in the Galam model of opinion dynamics and bottom-up hierarchical voting. A different probability for a flip against the local majority within the discussion group is associated with each ratio of majority / minority. The cases of groups of sizes 3 and 5 are investigated in detail. For hierarchical voting, the local flip corresponds to a `faithless elector', a representative who decides to vote against the choice of their electing group. Depending on the flip probabilities, the model exhibits a rich variety of pa…
