Binary Opinion Research Articles

Measuring the financial impact of equipment performance improvement: ISB and IEB metrics

PurposeEquipment performance helps the manufacturing sector achieve operational and financial improvements despite process variations. However, the literature lacks a clear index or metric to quantify the monetary advantages of enhanced equipment performance. Thus, the paper presents two innovative monetary performance measures to estimate the financial advantages of enhancing equipment performance by isolating the effect of manufacturing fluctuations such as product mix price, direct and indirect characteristics, and cost changes.Design/methodology/approachThe research provides two measures, ISB (Improvement Saving Benefits) and IEB (Improvement Earning Benefits), to assess equipment performance improvements. The effectiveness of the metrics is validated through a three stages approach, namely (1) experts' binary opinion, (2) sample, and (3) actual cases. The relevant data may be collected through accounting systems, purpose-built software, or electronic spreadsheets.FindingsThe findings suggest that both measures provide an effective cost–benefit analysis of equipment performance enhancement. The measure ISB indicates savings from performance increases when equipment capacity is greater than product demand. IEB is utilised when equipment capacity is less than product demand. Both measurements may replace the unitary cost variation, which is subject to manufacturing changes.Practical implicationsManufacturing businesses may utilise the ISB and IEB metrics to conduct a systematic analysis of equipment performance and to appreciate the financial savings perspective in order to emphasise profitability in the short and long term.Originality/valueThe study introduces two novel financial equipment performance improvement indicators that distinguish the effects of manufacturing variations. Manufacturing variations cause cost advantages from operational improvements to be misrepresented. There is currently no approach for manufacturing organisations to calculate the financial advantages of enhancing equipment performance while isolating production irregularities.

Opinion Evolution in Divided Community.

Our agent-based model of opinion dynamics concerns the current vast divisions in modern societies. It examines the process of social polarization, understood here as the partition of a community into two opposing groups with contradictory opinions. Our goal is to measure how mutual animosities between parties may lead to their radicalization. We apply a double-clique topology with both positive and negative ties to the model of binary opinions. Individuals are subject to social pressure; they conform to the opinions of their own clique (positive links) and oppose those from the other one (negative links). There is also a chance of acting independently, which alters the system’s behavior in various ways, depending on its magnitude. The results, obtained with both Monte-Carlo simulations and the mean-field approach, lead to two main conclusions: in such a system, there exists a critical quantity of negative relations that are needed for polarization to occur, and (rather surprisingly) independent actions actually support the process, unless their frequency is too high, in which case the system falls into total disorder.

Phase Transition in the Social Impact Model of Opinion Formation in Log-Normal Networks

People may change their opinions as a consequence of interacting with others. In the literature, this phenomenon is expressed as opinion formation and has a wide range of applications, including predicting social movements, predicting political voting results, and marketing. The interactions could be face-to-face or via online social networks. The social opinion phases are categorized into consensus, majority, and non-majority. In this research, we study phase transitions due to interactions between connected people with various noise levels using agent-based modeling and a computational social science approach. Two essential factors affect opinion formations: the opinion formation model and the network topology. We assumed the social impact model of opinion formation, a discrete binary opinion model, appropriate for both face-to-face and online interactions for opinion formation. For the network topology, scale-free networks have been widely used in many studies to model real social networks, while recent studies have revealed that most social networks fit log-normal distributions, which we considered in this study. Therefore, the main contribution of this study is to consider the log-normal distribution network topology in phase transitions in the social impact model of opinion formation. The results reveal that two parameters affect the phase transition: noise level and segregation. A non-majority phase happens in equilibrium in high enough noise level, regardless of the network topology, and a majority phase happens in equilibrium in lower noise levels. However, the segregation, which depends on the network topology, affects opinion groups’ population. A comparison with the scale-free network topology shows that in the scale-free network, which have a more segregated topology, resistance of segregated opinion groups against opinion change causes a slightly different phase transition at low noise levels. EI (External-Internal) index has been used to measure segregations, which is based on the difference between between-group (External) links and within-group (Internal) links.

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of s ge 2 states. As in the original binary q-voter model, which corresponds to s=2, at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability 1-p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states s>2 the model displays discontinuous phase transitions for any q>1, on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for q>5. Moreover, unlike the case of s=2, for s>2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

Optimal majority dynamics for the diffusion of an opinion when multiple alternatives are available

We consider opinion diffusion on social graphs where agents hold opinions and where social pressure leads them to conform to the opinion manifested by the majority of their neighbors. Within this setting, we look for dynamics that allows us to maximize the diffusion of a target opinion given the initial opinions of all agents. In particular, we focus on the setting where more than two opinions are available to the agents, and we show that the properties of this setting are entirely different from those characterizing the setting where agents hold binary opinions only. Indeed, while it is well-known that greedy dynamics are always optimal ones in the binary case, this is no longer true in our more general setting and—rather surprisingly—even if just three opinions are available. Moreover, while it is possible to decide in polynomial time if a dynamics leading to consensus exists when agents have two available opinions, the problem becomes computationally intractable with three opinions, regardless of the fraction of agents that have the target opinion as their initial opinion.

A Survey on Nonstrategic Models of Opinion Dynamics

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models.

A general model of binary opinions updating

We generalise Grabisch and Rusinowska (2013) to non-conformist societies. Agents in a network are iteratively picking a yes/no opinion, where updating stems from mutual influence. We introduce a notion of groups based on the signs of influence. We examine a few canonical societies, namely, conformist, communitarian, with leaders, with anti-conformist agents. We investigate stability issues. Any kind of opinion updating model can be hosted by our formalism, provided that: (i) alternatives are binary; (ii) opinion adoption is reversible and independent among agents; (iii) the process is Markovian and stationary; (iv) the number of agents is finite; (v) time is discrete.

A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks.

We analyze a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby q (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The q-voter model has been applied on multiplex networks, and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as on the value of q. The primary aim of this study is to examine phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters and . In a system of a duplex clique (i.e., two fully overlapped complete graphs) we find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phase transitions appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. The observation of successive phase transitions is a new quantity in binary state opinion formation models and we show that our analytical considerations are fully supported by Monte-Carlo simulations.

Voter and Majority Dynamics with Biased and Stubborn Agents

We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the preferred opinion. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is varTheta (log N), where N is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.

Emergence of Simple Characteristics for Heterogeneous Complex Social Agents

Models of interacting social agents often represent agents as very simple entities with a small number of degrees of freedom, as exemplified by binary opinion models for instance. Understanding how such simple individual characteristics may emerge from potentially much more complex agents is thus a natural question. It has been proposed recently in [E. Bertin, P. Jensen, C. R. Phys. 20, 329 (2019)] that some types of interactions among agents with many internal degrees of freedom may lead to a ‘simplification’ of agents, which are then effectively described by a small number of internal degrees of freedom. Here, we generalize the model to account for agent intrinsic heterogeneity. We find two different simplification regimes, one dominated by interactions, where agents become simple and identical as in the homogeneous model, and one where agents remain strongly heterogeneous although effectively with simple characteristics.

Multi-value opinion sharing based on information source influence in agent-based network

This paper proposes the information sharing algorithm for preventing propagation of wrong information in the agent-based network such as SNS, and aims at investigating the effectiveness of the proposed algorithm through the complex network such as a small world network. Towards practical applications, this paper extends the conventional opinion sharing model (OSM) to cope with the multi-value opinion from the binary opinion, and proposes the new algorithm for preventing propagation of wrong information to cope with the multi-value opinion. The intensive simulations of three types of the complex network have revealed that the accuracy of the correct opinion of agents in the proposed algorithm (called Self-information Weight Tuning (SWT)) reaches around 80% which is not affected by the number of opinion states in the multi-value opinions, while that of the conventional algorithm (called Autonomous Adaptive Tuning (AAT)) is lower than the proposed algorithm and decreases as the number of opinion states increases.

Symmetrical threshold model with independence on random graphs.

We study the homogeneous symmetrical threshold model with independence (noise) by pair approximation and Monte Carlo simulations on Erdős-Rényi and Watts-Strogatz graphs. The model is a modified version of the famous Granovetter's threshold model: with probability p a voter acts independently, i.e., takes randomly one of two states ±1; with complementary probability 1-p, a voter takes a given state, if a sufficiently large fraction (above a given threshold r) of individuals in its neighborhood is in this state. We show that the character of the phase transition, induced by the noise parameter p, depends on the threshold r, as well as graph's parameters. For r=0.5 only continuous phase transitions are observed, whereas for r>0.5 discontinuous phase transitions also are possible. The hysteresis increases with the average degree 〈k〉 and the rewriting parameter β. On the other hand, the dependence between the width of the hysteresis and the threshold r is nonmonotonic. The value of r, for which the maximum hysteresis is observed, overlaps pretty well with the size of the majority used for the descriptive norms in order to manipulate people within social experiments. We put the results obtained within this paper into a broader picture and discuss them in the context of two other models of binary opinions: the majority-vote and the q-voter model. Finally, we discuss why the appearance of social hysteresis in models of opinion dynamics is desirable.

Spatial early warning signals of social and epidemiological tipping points in a coupled behaviour-disease network

The resurgence of infectious diseases due to vaccine refusal has highlighted the role of interactions between disease dynamics and the spread of vaccine opinion on social networks. Shifts between disease elimination and outbreak regimes often occur through tipping points. It is known that tipping points can be predicted by early warning signals (EWS) based on characteristic dynamics near the critical transition, but the study of EWS in coupled behaviour-disease networks has received little attention. Here, we test several EWS indicators measuring spatial coherence and autocorrelation for their ability to predict a critical transition corresponding to disease outbreaks and vaccine refusal in a multiplex network model. The model couples paediatric infectious disease spread through a contact network to binary opinion dynamics of vaccine opinion on a social network. Through change point detection, we find that mutual information and join count indicators provided the best EWS. We also show the paediatric infectious disease natural history generates a discrepancy between population-level vaccine opinions and vaccine immunity status, such that transitions in the social network may occur before epidemiological transitions. These results suggest that monitoring social media for EWS of paediatric infectious disease outbreaks using these spatial indicators could be successful.

On the complexity of reasoning about opinion diffusion under majority dynamics

We study opinion diffusion on social graphs where agents hold binary opinions and where social pressure leads them to conform to the opinion manifested by the majority of their neighbors. We provide bounds relating the number of agents that suffice to spread an opinion to all other agents with the number of required propagation steps. Bounds are established constructively, via polynomial time algorithms that identify the agents that must act as seeds. In particular, we show that, on any given social graph G=(N,E), it is possible to efficiently identify a set formed by half of the agents that can lead to consensus in min⁡{⌊|N|/2⌋,even(G)+1} propagation steps, where even(G) is the number of agents with an even number of neighbors in G. The result marks the boundary of tractability, since we show that the existence of sets of seeds consisting of less than half of the agents depends on certain features of the underlying graphs, which are NP-hard to identify. In fact, other NP-hardness results emerge from our analysis. In particular, by closing a problem left open in the literature, we show that it is intractable to decide whether further stable configurations exist in addition to the “consensus” ones (where all agents hold the same opinion). Eventually, for all these problems related to reasoning about opinion diffusion, we show that islands of tractability can be identified by focusing on classes of tree-like social graphs.

Dynamics of opinion formation under majority rules on complex social networks

We study opinion dynamics on complex social networks where each individual holding a binary opinion on a certain subject may change her/his mind to match the opinion of the majority. Two rules of interactions between individuals, termed as classic majority and influence majority rules, respectively, are imposed on the social networks. The former rule allows each individual to adopt an opinion following a simple majority of her/his immediate neighbors, while the latter one lets each individual calculate the influence of each opinion and choose to follow the more influential one. In this calculation, the influences of different opinions are counted as the sum of the influences of their respective opinion holders in neighborhood area, where the influence of each individual is conveniently estimated as the number of social connections s/he has. Our study reveals that in densely-connected social networks, all individuals tend to converge to having a single global consensus. In sparsely-connected networks, however, the systems may exhibit rich properties where coexistence of different opinions, and more interestingly, multiple steady states of coexistence can be observed. Further studies reveal that low-degree and high-degree nodes may play different roles in formulating the final steady state, including multi-steady states, of the systems under different opinion evolution rules. Such observations would help understand the complex dynamics of opinion evolution and coexistence in social systems.

Binary opinion dynamics on signed networks based on Ising model

The evolution dynamics of public opinion is a hot issue in complex networks research. And the Ising model is the earliest classic dynamic model of public opinion. Although signed networks can describe amicable and antagonistic relationship in complex real-world systems accurately, and the research on dynamic process of public opinion evolution on signed networks is valuable, few people have paid attention to that. Previous methods for opinion diffusion cannot be applied to signed network directly, which ignore the important information contained in the negative edges. In this paper, the binary opinion dynamics on signed networks has been modeled by aid of the Ising model. The model is applied both to the synthetic and real-world signed networks. We observe that the proportion and distribution of negative edges have a fundamental effect on the evolutionary result of public opinion on signed networks. There exists the critical ratio. When the proportion of negative edges in the network exceeds the critical ratio, there appears to be a completely different evolutionary result, and the distribution of negative edges affects the value of the critical ratio. In addition, we study the network structural balance in the evolutionary process of opinion on signed networks as complementary. Our findings can deepen the understanding of the evolutionary process of binary opinion in real signed social systems.

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 > 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.

Opinion influence and evolution in social networks: A Markovian agents model

In this paper, the effect on collective opinions of filtering algorithms managed by social network platforms is modeled and investigated. A stochastic multi-agent model for opinion dynamics is proposed, that accounts for a centralized tuning of the strength of interaction between individuals. The evolution of each individual opinion is described by a Markov chain, whose transition rates are affected by the opinions of the neighbors through influence parameters. The properties of this model are studied in a general setting as well as in interesting special cases. A general result is that the overall model of the social network behaves like a high-dimensional Markov chain, which is viable to Monte Carlo simulation. Under the assumption of identical agents and unbiased influence, it is shown that the influence intensity affects the variance, but not the expectation, of the number of individuals sharing a certain opinion. Moreover, a detailed analysis is carried out for the so-called Peer Assembly, which describes the evolution of binary opinions in a completely connected graph of identical agents. It is shown that the Peer Assembly can be lumped into a birth–death chain that can be given a complete analytical characterization. Both analytical results and simulation experiments are used to highlight the emergence of particular collective behaviors, e.g. consensus and herding, depending on the centralized tuning of the influence parameters.

Think then act or act then think?

We introduce a new agent-based model of opinion dynamics in which binary opinions of each agent can be measured and described regarding both pre- and post-influence at both of two levels, public and private, vis-à-vis the influence source. The model combines ideas introduced within the q-voter model with noise, proposed by physicists, with the descriptive, four-dimensional model of social response, formulated by social psychologists. We investigate two versions of the same model that differ only by the updating order: an opinion on the public level is updated before an opinion on the private level or vice versa. We show how the results on the macroscopic scale depend on this order. The main finding of this paper is that both models produce the same outcome if one looks only at such a macroscopic variable as the total number of the individuals with positive opinions. However, if also the level of internal harmony (viz., dissonance) is measured, then significant, qualitative differences are seen between these two versions of the model. All results were obtained simultaneously within Monte Carlo simulations and analytical calculations. We discuss the importance of our studies and findings from three points of view: the theory of phase transitions, agent-based modeling of social systems, and social psychology.

Group-based rewiring rules of binary opinion competition dynamics

The dynamics of competing opinions on networks has attracted multi-disciplinary research. Most modelling approaches assume uniform or heterogeneous behaviour among all individuals, while the role of distinctive group behaviour is rarely addressed. Here, we consider competition occurring between two opinion groups with bound rewiring rules, i.e., opinion-preferred rewiring, degree-preferred rewiring and random rewiring. When two opinions share a balanced initial proportion, opinion-preferred rewiring is superior to the other rules under low rewiring rates, and coexistence occurs under high rewiring rates. For unbalanced proportions, the best response rule for the minority/majority is unfixed, and this depends on the initial proportion and rewiring frequency. Furthermore, we find evolution processes for all competing cases belong to two categories. Evolution Category I shows an obvious correlation between opinion proportions and the density of discordant edges (connecting nodes with different opinions), and these trends can be effectively described by numerical approximations. However, for Evolution Category II, no such correlation exists for individuals or linking pairs, and an analysis of local structures reveals the emergence of large numbers of open triads with the same opinions, denoting group prevalence. This work broadens the understanding of opinion competition and inspires exploring group strategies employed in social dynamic systems.