Majority-vote Model Research Articles

Non-equilibrium BCS model on Apollonian networks

We study the phase transition in a discrete opinion dynamics model on an Apollonian network, where mutual interactions can be both positive and negative depending on the noise parameter q. We have characterized the critical exponents of the phase transitions through the Monte Carlo simulations and finite-size scaling analysis. Our finds attest that different from the equilibrium models, such as Ising and Potts on Apollonian network that do not present phase transition, the kinetic model report does. Moreover, we have included one additional aspect on the Apollonian network, the effect of redirecting a fraction of p of the network’s links. On this redirected network, we obtained the exponents ratio β∕ν, γ∕ν, and 1∕ν for several values of rewiring probability p. Similar to this model’s results on free-scale networks, the effective dimensionality of the system found was Deff≈1.0 for all values of p. The results presented here demonstrate that kinetic models of discrete opinion dynamics belong to a different universality class as the equilibrium Ising Model on Apollonian networks. It is noticed that the kinetic model study here and the majority-vote model on Apollonian networks are in the same universality class, for a rewiring probability lower than 0.5. Above p=0.5, the critical exponents are different from those found in the majority-vote model on Apollonian networks.

Majority-vote model with degree-weighted influence on complex networks.

We study the phase transition of the degree-weighted majority vote (DWMV) model on Erdős-Rényi networks (ERNs) and scale-free networks (SFNs). In this model, a weight parameter α adjusts the level of influence of each node on its connected neighbors. Through the Monte Carlo simulations and the finite-size scaling analysis, we find that the DWMV model on ERNs and SFNs with degree exponents λ>5 belongs to the mean-field Ising universality class, regardless of α. On SFNs with 3<λ<5 the model belongs to the Ising universality class only when α=0. For α>0 we find that the critical exponents continuously change as α increases from α=0. However, on SFNs with λ<3 we find that the model undergoes a continuous transition only for α=0, but the critical exponents significantly deviate from those for the mean-field Ising model. For α>0 on SFNs with λ<3 the model is always in the disordered phase.

Non-Markovian majority-vote model.

Non-Markovian dynamics pervades human activity and social networks and it induces memory effects and burstiness in a wide range of processes including interevent time distributions, duration of interactions in temporal networks, and human mobility. Here, we propose a non-Markovian majority-vote model (NMMV) that introduces non-Markovian effects in the standard (Markovian) majority-vote model (SMV). The SMV model is one of the simplest two-state stochastic models for studying opinion dynamics, and displays a continuous order-disorder phase transition at a critical noise. In the NMMV model we assume that the probability that an agent changes state is not only dependent on the majority state of his neighbors but it also depends on his age, i.e., how long the agent has been in his current state. The NMMV model has two regimes: the aging regime implies that the probability that an agent changes state is decreasing with his age, while in the antiaging regime the probability that an agent changes state is increasing with his age. Interestingly, we find that the critical noise at which we observe the order-disorder phase transition is a nonmonotonic function of the rate β of the aging (antiaging) process. In particular the critical noise in the aging regime displays a maximum as a function of β while in the antiaging regime displays a minimum. This implies that the aging/antiaging dynamics can retard/anticipate the transition and that there is an optimal rate β for maximally perturbing the value of the critical noise. The analytical results obtained in the framework of the heterogeneous mean-field approach are validated by extensive numerical simulations on a large variety of network topologies.

Stochastic Resonance in the Majority Vote Model on Scale-Free Networks

Stochastic Resonance in the Majority Vote Model on Scale-Free Networks

Majority-vote model with limited visibility: An investigation into filter bubbles

The dynamics of opinion formation in a society is a complex phenomenon where many variables play essential roles. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the algorithms promote marketing strategies, but can also facilitate the formation of filters bubbles in which a user is most likely exposed to opinions that conform to their own. In the two-state majority-vote model, an individual adopts an opinion contrary to the majority of its neighbors with probability q, defined as the noise parameter. Here, we introduce a visibility parameter V in the dynamics of the majority-vote model, which equals the probability of an individual ignoring the opinion of each one of its neighbors. For V=0.5 each individual will, on average, ignore the opinion of half of its neighboring nodes. We employ Monte Carlo simulations to calculate the critical noise parameter as a function of the visibility qc(V) and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the visibility parameter, such that a lower value of V favors dissensus. Via finite-size scaling analysis we obtain the critical exponents of the model, which are visibility-independent, and show that the model belongs to the Ising universality class. We compare our results to the case of a network submitted to a static site dilution and find that the limited visibility model is a more subtle way of inducing opinion polarization in a social network.

Rosetta Machine Learning Models Accurately Classify Positional Effects of Thioamides on Proteolysis.

Thioamide substitutions of the peptide backbone have been shown to stabilize therapeutic and imaging peptides toward proteolysis. In order to rationally design thioamide modifications, we have developed a novel Rosetta custom score function to classify thioamide positional effects on proteolysis in substrates of serine and cysteine proteases. Peptides of interest were docked into proteases using the FlexPepDock application in Rosetta. Docked complexes were modified to contain thioamides parametrized through the creation of custom atom types in Rosetta based on ab intio simulations. Thioamide complexes were simulated, and the resultant structural complexes provided features for machine learning classification as the decomposed values of the Rosetta score function. An ensemble, majority voting model was developed to be a robust predictor of previously unpublished thioamide proteolysis holdout data. Theoretical control simulations with pseudo-atoms that modulate only one physical characteristic of the thioamide show differential effects on prediction accuracy by the optimized voting classification model. These pseudo-atom model simulations, as well as statistical analyses of the full thioamide simulations, implicate steric effects on peptide binding as being primarily responsible for thioamide positional effects on proteolytic resistance.

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Ferromagnetic and spin-glass-like transitions in nonequilibrium spin models in contact with two thermal baths with different temperatures are investigated. The models comprise the Sherrington-Kirkpatrick model and the dilute spin glass model which are the Ising models on complete and random graphs, respectively, with edges corresponding, with certain probability, to positive and negative exchange integrals. The spin flip rates are combinations of two Glauber rates at the two temperatures, and by varying the coefficients of this combination probabilities of contact of the model with each thermal bath and thus the level of thermal noise in the model are changed. Particular attention is devoted to the majority vote model in which one of the two above-mentioned temperatures is zero and the other one tends to infinity. Only in rare cases such nonequilibrium models can be mapped onto equilibrium ones at certain effective temperature. Nevertheless, Monte Carlo simulations show that transitions from the paramagnetic to the ferromagnetic and spin-glass-like phases occur in all cases under study as the level of thermal noise is varied, and the phase diagrams resemble qualitatively those for the corresponding equilibrium models obtained with varying temperature. Theoretical investigation of the model on complete and random graphs is performed using the TAP equations as well as mean-field and pair approximations, respectively. In all cases theoretical calculations yield reasonably correct predictions concerning location of the phase border between the paramagnetic and ferromagnetic phases. In the case of the spin-glass-like transition only qualitative agreement between theoretical and numerical results is achieved using the TAP equations, and the mean-field and pair approximations are not suitable for the study of this transition. The obtained results can be interesting for modeling opinion formation by means of the majority-vote and related models and suggest that in the presence of negative interactions between agents, apart from the ferromagnetic phase corresponding to consensus formation, spin-glass-like phase can occur in the society characterized by local rather than long-range ordering.Graphical abstract

A numerical study on efficient jury size

For judicial democracy, many societies adopt jury trials, where verdicts are made by a unanimous vote of, conventionally, 12 lay citizens. Here, using the majority-vote model, we show that such jury sizes achieve the best balance between the accuracy of verdicts and the time spent for unanimous decision-making. First, we identify two determinants of the efficient jury size: the opinion homogeneity in a community decreases the optimal jury size by affecting the accuracy of verdicts; the anti-conformity tendency in the community also reduces the efficient jury size by prolonging the time to reach unanimous verdicts. Moreover, we find an inverse correlation between these two determinants, which prevents over-shrinking and excessive expansion of the efficient jury size. Finally, by applying these findings into real-life settings, we narrow down the efficient jury size to 11.8 ± 3.0. Given that such a simple toy model can explain the jury sizes in the actual societies, the number of jurors may have been implicitly optimised for efficient unanimous decision-making throughout human history.

A Reliable Weighting Scheme for the Aggregation of Crowd Intelligence to Detect Fake News

Social networks play an important role in today’s society and in our relationships with others. They give the Internet user the opportunity to play an active role, e.g., one can relay certain information via a blog, a comment, or even a vote. The Internet user has the possibility to share any content at any time. However, some malicious Internet users take advantage of this freedom to share fake news to manipulate or mislead an audience, to invade the privacy of others, and also to harm certain institutions. Fake news seeks to resemble traditional media to establish its credibility with the public. Its seriousness pushes the public to share them. As a result, fake news can spread quickly. This fake news can cause enormous difficulties for users and institutions. Several authors have proposed systems to detect fake news in social networks using crowd signals through the process of crowdsourcing. Unfortunately, these authors do not use the expertise of the crowd and the expertise of a third party in an associative way to make decisions. Crowds are useful in indicating whether or not a story should be fact-checked. This work proposes a new method of binary aggregation of opinions of the crowd and the knowledge of a third-party expert. The aggregator is based on majority voting on the crowd side and weighted averaging on the third-party side. An experimentation has been conducted on 25 posts and 50 voters. A quantitative comparison with the majority vote model reveals that our aggregation model provides slightly better results due to weights assigned to accredited users. A qualitative investigation against existing aggregation models shows that the proposed approach meets the requirements or properties expected of a crowdsourcing system and a voting system.

Three-State Majority-vote Model on Scale-Free Networks and the Unitary Relation for Critical Exponents

We investigate the three-state majority-vote model for opinion dynamics on scale-free and regular networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability 1 − q, and different to it with probability q. The parameter q is called the noise parameter of the model. We build a network of interactions where z neighbors are selected by each added site in the system, a preferential attachment network with degree distribution k−λ, where λ = 3 for a large number of nodes N. In this work, z is called the growth parameter. Using finite-size scaling analysis, we obtain that the critical exponents beta /bar{nu } and gamma /bar{nu } associated with the magnetization and the susceptibility, respectively. Using Monte Carlo simulations, we calculate the critical noise parameter qc as a function of z for the scale-free networks and obtain the phase diagram of the model. We find that the critical exponents add up to unity when using a special volumetric scaling, regardless of the dimension of the network of interactions. We verify this result by obtaining the critical noise and the critical exponents for the two and three-state majority-vote model on cubic lattice networks.

Robust Light-Weight Magnetic-Based Door Event Detection with Smartphones

Doors as densely-deployed natural landmarks play an important role in improving indoor positioning systems. However, the state-of-the-art door event detection works are based on either vision or infrastructure, thus incurring non-trivial device or management cost. To address these problems, we present a Light-weight Magnetic-based Door Event Detection method, called LMDD. It leverages built-in magnetic sensors of common smartphones to achieve infrastructure-free door event detection. After analyzing the special features of sensors’ readings changes caused by the door, we design LMDD scheme with three main components, including data acquisition, events identification and events denoising. Moreover, an improved and robust door event detection framework based on a majority-voting model is proposed to fuse multiple-dimensional sensing data from non-magnetic built-in sensors. We have implemented a prototype of LMDD on Android-based platform. Experimental results show that LMDD with only magnetic sensor achieves door event detection accuracy of around 80 percent on average, ranging from 70 to 87 percent in various typical indoor environments. The enhanced LMDD based on the fusion of heterogeneous sensors can achieve a much higher door event detection accuracy of 90 percent on average.

Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

Entropy production as a tool for characterizing nonequilibrium phase transitions

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has been revealed to be an important concept for filling this gap since it vanishes identically for equilibrium systems and is positive for the nonequilibrium case. Based on distinct and general arguments, the characterization of phase transitions in terms of the entropy production is presented. Analysis for discontinuous and continuous phase transitions has been undertaken by taking regular and complex topologies within the framework of mean-field theory (MFT) and beyond the MFT. A general description of entropy production portraits for Z_{2} ("up-down") symmetry systems under the MFT is presented. Our main result is that a given phase transition, whether continuous or discontinuous has a specific entropy production hallmark. Our predictions are exemplified by an icon system, perhaps the simplest nonequilibrium model presenting an order-disorder phase transition and spontaneous symmetry breaking: the majority vote model. Our work paves the way to a systematic description and classification of nonequilibrium phase transitions through a key indicator of system irreversibility.

Majority-vote dynamics on multiplex networks with two layers

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 processes will be studied on multiplex networks with two layers 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 voters on single-network system. The AND-model reaches the largest consensus below the critical noise parameter qc. It needs, however, much longer time to reach consensus than other models. In the vicinity of the transition point, the consensus collapses abruptly. The OR-model attains smaller level of consensus than the AND-rule but reaches the consensus more quickly. Its consensus transition is continuous. The numerical simulation results are supported qualitatively by analytical calculations based on the approximate master equation.

Tax Evasion Dynamics via Kinetic Models of Opinion Dynamics

The socioeconomic phenomena as tax evasion in agent-based community can be studied numerically through the Zaklan model (ZM). The ZM has been con_gured as an excellent tool to control the tax evasion uctuations in communities with agents or individuals that can be considered tax evaders or honest. The dynamic of temporal evolution of the ZM was studied initially via the equilibrium Ising model (IM), non-equilibrium Majority-vote model (MVM) and recently via a three-state kinetic agent-based model. Here, through Monte Carlo simulations, we study the problem of the tax evasion uctuations using a discrete version of the kinetic model of opinion dynamics (BCS) in the dynamic of the temporal evolution of the ZM. Unlike previous models cited here in the BCS model, the interactions between agents occur in pairs. Then, we found that the BCS model is as e_cient as the IM and MVM in controlling the tax evasion uctuations. This control is even better when we use strong punishment values k even for low audit probabilities pa.

Critical behavior of majority vote model on two-dimensional quasiperiodic tilings

We investigated majority vote model coupled with quasiperiodic tilings by using both Monte Carlo and finite size scaling techniques. We obtained numerically the following averages: Binder cumulant , order parameter , defined as the averaged opinion balance, and its respective susceptibility . Our numerical results suggest that the system falls in two-dimensional Ising universality class. In addition, our results are in agreement with Harris–Barghathi–Vojta criterion, which states that two-dimensional quasiperiodic ordering is irrelevant and does not change any of the critical exponents.

Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so‐called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and possesses an up‐down symmetry, which makes it similar to other binary opinion models with a single‐flip dynamics, such as the majority‐vote and the q‐voter models. Because within the majority‐vote model with independence only continuous phase transitions are observed, whereas within the q‐voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean‐field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed if the threshold r = 0.5, which corresponds to the majority‐vote model, an order‐disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r &gt; 0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.

Majority-vote Model with Independent Agents on Complex Networks

Majority-vote Model with Independent Agents on Complex Networks

MHLM Majority Voting Based Hybrid Learning Model for Multi-Document Summarization

Text summarization from multiple documents is an active research area in the current scenario as the data in the World Wide Web (WWW) is found in abundance. The text summarization process is time-consuming and hectic for the users to retrieve the relevant contents from this mass collection of the data. Numerous techniques have been proposed to provide the relevant information to the users in the form of the summary. Accordingly, this article presents the majority voting based hybrid learning model (MHLM) for multi-document summarization. First, the multiple documents are subjected to pre-processing, and the features, such as title-based, sentence length, numerical data and TF-IDF features are extracted for all the individual sentences of the document. Then, the feature set is sent to the proposed MHLM classifier, which includes the Support Vector Machine (SVM), K-Nearest Neighbors (KNN), and Neural Network (NN) classifiers for evaluating the significance of the sentences present in the document. These classifiers provide the significance scores based on four features extracted from the sentences in the document. Then, the majority voting model decides the significant texts based on the significance scores and develops the summary for the user and thereby, reduces the redundancy, increasing the quality of the summary similar to the original document. The experiment performed with the DUC 2002 data set is used to analyze the effectiveness of the proposed MHLM that attains the precision and recall at a rate of 0.94, f-measure at a rate of 0.93, and ROUGE-1 at a rate of 0.6324.

Flexible service discovery based on multiple matching algorithms

Traditional web service discovery approaches rely on logic or non-logic matching techniques. In general, logic approaches can achieve satisfactory precision levels, but they result in modest recall scores. In contrast, non-logic approaches may ensure more balanced scores in terms of recall and precision, but they need additional aggregation schemes or optimisation methods. To improve the discovery performance, we need to combine multiple matching algorithms and fuse their results into a single ranked list of services. This combination must avoid the well-known side effects of fusion, such as overfitting or noise sensitivity. To tackle the service-discovery issue, we propose a solution based on two key ideas: first, we propose a majority voting model based on the 'Condorcet' paradigm to fuse a set of individual ranked lists (provided by the matching functions). Second, we leverage a probabilistic extension of the dominance relationship to ensure comparison between the services. The experimental evaluations indicate the proposed solution, 'probabilistic Condorcet', outperforms all individual matching functions, as well as many concurrent fusion algorithms.