Opinion Dynamics

Messages conveyed by media act as a major drive in shaping attitudes and inducing opinion shift. On the other hand, individuals are strongly affected by peer pressure while forming their own judgment. We solve a general model of opinion dynamics where individuals either hold one of two alternative opinions or are undecided and interact pairwise while exposed to an external influence. As media pressure increases, the system moves from pluralism to global consensus; four distinct classes of collective behavior emerge, crucially depending on the outcome of direct interactions among individuals holding opposite opinions. Observed nontrivial behaviors include hysteretic phenomena and resilience of minority opinions. Notably, consensus could be unachievable even when media and microscopic interactions are biased in favor of the same opinion: The unfavored opinion might even gain the support of the majority.

En masse data mining, aided by the popularity of web-based social networks, has become one of the more pressing issues of modern society. Where should the line be drawn? Increasingly, the decisions that
affect our lives are being made not by humans, but by mathematical models. The models being used today are opaque, unregulated, and
incontestable, even when they’re wrong. Understanding how people interact is no easy task – this is why we mostly rely on simplified models. As it turns out, the instruments of statistical physics can help refine our models. In my Bachelor’s thesis, I propose a new model of how
opinions spread in a society. The model draws heavily from the Ising model of ferromagnetism.

As a key sub-field of social dynamics and sociophysics, opinion dynamics utilizes mathematical and physical models and the agent-based computational modeling tools, to investigate the spreading of opinions in a collection of human beings. This research field stems from various disciplines in social sciences, especially the social influence models developed in social psychology and sociology. A multidisciplinary review is given in this paper, attempting to keep track of the historical development of the field and to shed light on its future directions. In the review, we firstly discuss the disciplinary origins of opinion dynamics, showing that the combination of the social processes, which are conventionally studied in social sciences, and the analytical and computational tools, which are developed in mathematics, physics and complex system studies, gives birth to the interdisciplinary field of opinion dynamics. The current state of the art of opinion dynamics is then overviewed, with the research progresses on the typical models like the voter model, the Sznajd model, the culture dissemination model, and the bounded confidence model being highlighted. Correspondingly, the future directions of this academic field are envisioned, with an advocation for closer synthesis of the related disciplines.

The aim of the research is to give a contribution and an insight on the complex field of stakeholder involvement in transport planning, by analysing the role of decision-support methods and agent-based modelling in guiding a participation process.
The approach is twofold: from one side it is about to deeply understand the process of making a collective decision, by studying how the interaction among different actors can lead to a convergence of opinions towards a shared collective decision. From the other side, it is based on finding appropriate decision-support methods to help the group decision-making process.
Agent-based modelling and simulations have been used, in order to guide real participation processes and predict the results of an interaction process, and group multi criteria decision-making methods, to help taking consistent decisions based on several judgment criteria. The results of the research should help decision-makers and practitioners in dealing with multiple stakeholders and complex decisions and guiding the participation process.

1.1 Computer simulation of opinion dynamics (consensus models) (Axelrod 1997; Deffuant 2000; Deffuant 2002; Weisbuch 2002; Hegselmann 2002; Hegselmann 2004; Krause 1997; Sznajd-Weron 2000; Stauffer 2000; Stauffer 2002; Galam 1990; Galam 1997; Stauffer ...

The dynamics of a one dimensional Ising spin system is investigated using three families of local update rules, the Galam majority rules, Glauber inflow influences and Sznadj outflow drives. Given an initial density p of up spins the probability to reach a final state with all spins up is calculated exactly for each choice. The various formulas are compared to a series of previous calculations obtained analytically using the Kirkwood approximation. They turn out to be identical. The apparent discrepancy with the Galam unifying frame is addressed. The difference in the results seems to stem directly from the implementation of the local update rule used to perform the associated numerical simulations. The findings lead to view the non stepwise exit probability as an artifact of the one dimensional finite size system with fixed spins. The suitability and the significance to perform numerical simulations to model social behavior without solid constraints is discussed and the question of...

In a situation of peer disagreement, peers are usually assumed to share the same evidence. However they might not share the same evidence for the epistemic system used to process the evidence. This synchronic complication of the peer disagreement debate suggested by Goldman (In Feldman R, Warfield T (eds) (2010) Disagreement. Oxford University Press, Oxford, pp 187–215) is elaborated diachronically by use of a simulation. The Hegselmann–Krause model is extended to multiple epistemic systems and used to investigate the role of consensus and difference splitting in peer disagreement. I find that the very possibility of multiple epistemic systems downgrades the epistemic value of consensus and makes difference splitting a suboptimal strategy.

Journal of Artificial Societies and Social Simulation vol. 9, no. 3. 2006 http://jasss.soc.surrey.ac .uk/9/3/10.html ... First Steps towards a Computer Aided Social Epistemology ... Rainer Hegselmann Department of Philosophy, University Bayreuth ... Ulrich Krause Department of ...

This paper introduces a logic to reason about a well-known model of opinion dynamics in social networks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of  Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis.

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data.

In 1997, Robert Axelrod wondered in a highly influential paper "If people tend to become more alike in their beliefs, attitudes, and behavior when they interact, why do not all such differences eventually disappear?" Axelrod's question highlighted an ongoing quest for formal theoretical answers joined by researchers from a wide range of disciplines. Numerous models have been developed to understand why and under what conditions diversity in beliefs, attitudes and behavior can co-exist with the fact that very often in interactions, social influence reduces differences between people. Reviewing three prominent approaches, we discuss the theoretical ingredients that researchers added to classic models of social influence as well as their implications. Then, we propose two main frontiers for future research. First, there is urgent need for more theoretical work comparing, relating and integrating alternative models. Second, the field suffers from a strong imbalance between a proliferation of theoretical studies and a dearth of empirical work. More empirical work is needed testing and underpinning micro-level assumptions about social influence as well as macro-level predictions. In conclusion, we discuss major roadblocks that need to be overcome to achieve progress on each frontier. We also propose that a new generation of empirically-based computational social influence models can make unique contributions for understanding key societal challenges, like the possible effects of social media on societal polarization.

This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as $k$--dimensional bit--strings. Individuals interact if the difference in the opinion strings is below a defined similarity threshold $d_I$. Depending on $d_I$, different behaviour of the population is observed: low values result

A local culture denotes a commonly shared behaviour within a cluster of firms. Similar to social norms or conventions, it is an emergent feature resulting from the firms' interaction in an economic network. To model these dynamics, we consider a distributed agent population, representing e.g. firms or individuals. Further, we build on a continuous opinion dynamics model with bounded confidence ($\epsilon$), which assumes that two agents only interact if differences in their behaviour are less than $\epsilon$. Interaction results in more similarity of behaviour, i.e. convergence towards a common mean. This framework is extended by two major concepts: (i) The agent's in-group consisting of acquainted interaction partners is explicitly taken into account. This leads to an effective agent behaviour reflecting that agents try to continue to interact with past partners and thus to keep sufficiently close to them. (ii) The in-group network structure changes over time, as agents can form new links to other agents with sufficiently close effective behaviour or delete links to agents no longer close in behaviour. Thus, our model provides a feedback mechanism between the agents' behaviour and their in-group structure. Studying its consequences by means of agent-based computer simulations, we find that for narrow-minded agents (low $\epsilon$) the additional feedback helps to find consensus more often, whereas for open-minded agents (high $\epsilon$) this does not hold. This counterintuitive result is explained by simulations of the network evolution.

Empirical findings from social psychology show that sometimes people show favoritism toward in-group members in order to reach a global consensus, even against individuals' own preferences (e.g., altruistically or deontically). Here we integrate ideas and findings on in-group favoritism, opinion dynamics, and radicalization using an agent-based model entitled cooperative bounded confidence (CBC). We investigate the interplay of homophily, rejection, and in-group cooperation drivers on the formation of opinion clusters and the emergence of extremist, radical opinions. Our model is the first to explicitly explore the effect of in-group favoritism on the macro-level, collective behavior of opinions. We compare our model against the two-dimentional bounded confidence model with rejection mechanism, proposed by Huet et al. (2008), and find that the number of opinion clusters and extremists is reduced in our model. Moreover, results show that group influence can never dominate homophilous and rejecting encounters in the process of opinion cluster formation. We conclude by discussing implications of our model for research on collective behavior of opinions emerging from individuals' interaction.

Abstract. We study the Deffuant et al model for continuous-opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending on a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main ...

Abstract: Despite the increasing diffusion of the Internet technology, TV remains the principal medium of communication. People's perceptions, knowledge, beliefs and opinions about matter of facts get (in) formed through the information reported on by the mass-media. However, a single source of information (and consensus) could be a potential cause of anomalies in the structure and evolution of a society. Hence, as the information available (and the way it is reported) is fundamental for our perceptions and opinions, the definition ...

This paper focuses on the relationship between two "everyday" beliefs about social systems. The first is that the variable attributes of individuals (attitudes, beliefs, opinions) in a social system do not typically tend to unanimous indifference. The second is that the attitudes, beliefs and opinions of individuals in a social system undergo some mutual influence. This paper uses simulation to explore a number of different mechanisms for such influence and shows that many of them have a strong tendency to unanimous indifference. It also explores some mechanisms that avoid this phenomenon. The intention is to suggest individual interaction and decision mechanisms for individuals that are behaviourally plausible without leading to implausible collective behaviour (unanimous indifference). The paper also attempts to situate its findings within the existing literature.

The research on opinion dynamics in social networks and opinion influence models often sufer from a lack of grounding in social theories and also of empirical data validation. The current availability of large datasets and the ease by which Internet social data can now be collected makes some validation of theoretical social models a less dificult task. Starting by a state-of-the-art of the research and practice concerning political opinion dynamics in social networks, we identify the main strengths and weaknesses of the domain.We then propose a novel method for uncovering political opinion dynamics using on-line data gathering. The method includes three distinct phases: (1) data collection, (2) multiagent modelling (3) validation. Specifically, we tested the signicance of Social Impact Theory, originally proposed by Latane (1981) and Brownian Agent modelling, proposed by Schweitzer (2002), for characterizing political opinion formation during electoral periods. These two models were tested using more than 100.000 tweets collected from the 30th October to the 21st January 2011 and from 27th of March to the 6th of June 2011, concerning the Portuguese presidential and legislative elections occurred in 2011. Following the data collection, two distinct on-line communities were inspected: the general Twitter user community and the traditional news media twitter feeds. The opinion dynamics, known from Twitter population during the campaigns, was simulated with grid adjustment of model parameters. This operation was performed on separate empirical series respecting the talk about the six electoral candidates and parties. The complete process allowed concluding about the explanatory power of Social Impact Theory and Brownian Agents, and, on the other side, allowed characterizing opinion dynamics in this specic case study. This article details each phase of the method, illustrated using the dataset available at http://work.theobservatorium.eu/presid2011.

"Probing deeper into the existing issues regarding the exit probability (EP) in one dimensional dynamical models,  we consider several  models where the states are represented by Ising spins  and the  information flows inwards. At zero temperature, these systems evolve to either of two absorbing states. The exit probability $E(x)$, which is the probability that the system ends up with all spins up starting with $x$ fraction of up spins  is found to have the general form  $E(x) = x^\alpha/\left[x^\alpha + (1-x)^\alpha\right]$.  The exit probability exponent $\alpha$ strongly depends on $r$, the range of interaction, the symmetry of the model and the induced  fluctuation. Even in a nearest neighbour model, nonlinear form of EP can be obtained by controlling the fluctuations and for the same range, different models give different results for $\alpha$. Non-universal behaviour of the  exit probability is thus clearly established and the results are compared to existing studies in models with outflow dynamics to distinguish the two dynamical scenarios. "

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with ...