The undecided have the key: Interaction-driven opinion dynamics in a three state model

The effects of interpersonal interactions on individual's agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a given issue. This field, which has been a longstanding concern of sociologists and psychologists, has been extended into an area of experimental social psychology, and even has attracted the attention of physicists and mathematicians. In this article, we present a novel model of opinion formation in which agents may either have a strict preference for a choice, or be undecided. The opinion shift emerges during interpersonal communications, as a consequence of a cumulative process of conviction for one of the two extremes opinions through repeated interactions. There are two main ingredients which play key roles in determining the steady state: the initial fraction of undecided agents and the conviction's sensitivity in each interaction. As a function of these two parameters, the model presents a wide range of possible solutions, as for instance, consensus of each opinion, bi-polarisation or convergence of undecided individuals. We found that a minimum fraction of undecided agents is crucial not only for reaching consensus of a given opinion, but also to determine a dominant opinion in a polarised situation. In order to gain a deeper comprehension of the dynamics, we also present the theoretical master equations of the model.Comment: 21 pages, 6 figure

Modeling Opinion Dynamics: Theoretical analysis and continuous approximation

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion. In this case, the agreement is reached because the new arguments are incorporated. In this paper we deal with a simple model of opinion formation with such persuasion dynamics, and we find the exact analytical solutions for both, long and short range interactions. A novel theoretical approach has been used in order to solve the master equations of the model with non-local kernels. Simulation results demonstrate an excellent agreement with results obtained by the theoretical estimation.Comment: 15 pages, 3 figure

Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP).Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When $j$, the ratio of the social influene strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of $j$ above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria.Beyond this first result, we exhibit the {\em generic} properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend {\em only} on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite).The main results are summarized as {\em phase diagrams} in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.discrete choice; social influence; externalities; heterogeneous agents; socioeconomic behavior

Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP). Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When j, the ratio of the social influence strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of j above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria. Beyond this first result, we exhibit the generic properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend only on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite). The main results are summarized as phase diagrams in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.Comment: 42 pages, 15 figure

Latent dirichlet allocation model for world trade analysis

International trade is one of the classic areas of study in economics. Its empirical analysis is a complex problem, given the amount of products, countries and years. Nowadays, given the availability of data, the tools used for the analysis can be complemented and enriched with new methodologies and techniques that go beyond the traditional approach. This new possibility opens a research gap, as new, data-driven, ways of understanding international trade, can help our understanding of the underlying phenomena. The present paper shows the application of the Latent Dirichlet allocation model, a well known technique in the area of Natural Language Processing, to search for latent dimensions in the product space of international trade, and their distribution across countries over time. We apply this technique to a dataset of countries exports of goods from 1962 to 2016. The results show that this technique can encode the main specialisation patterns of international trade. On the countrylevel analysis, the findings show the changes in the specialisation patterns of countries over time. As traditional international trade analysis demands expert knowledge on a multiplicity of indicators, the possibility of encoding multiple known phenomena under a unique indicator is a powerful complement for traditional tools, as it allows top-down data-driven studies.Fil: Kozlowski, Diego. University of Luxembourg; LuxemburgoFil: Semeshenko, Viktoriya. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Interdisciplinario de Economía Política de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Instituto Interdisciplinario de Economía Política de Buenos Aires; ArgentinaFil: Molinari, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Interdisciplinario de Economía Política de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Instituto Interdisciplinario de Economía Política de Buenos Aires; Argentin

Cooperation and Defection at the Crossroads

We study a simple traffic model with a non-signalized road intersection. In this model the car arriving from the right has precedence. The vehicle dynamics far from the crossing are governed by the rules introduced by Nagel and Paczuski, which define how drivers behave when braking or accelerating. We measure the average velocity of the ensemble of cars and its flow as a function of the density of cars on the roadway. An additional set of rules is defined to describe the dynamics at the intersection assuming a fraction of drivers that do not obey the rule of precedence. This problem is treated within a gametheory framework, where the drivers that obey the rule are cooperators and those who ignore it are defectors. We study the consequences of these behaviors as a function of the fraction of cooperators and defectors. The results show that cooperation is the best strategy because it maximizes the flow of vehicles and minimizes the number of accidents. A rather paradoxical effect is observed: for any percentage of defectors the number of accidents is larger when the density of cars is low because of the higher average velocity.Fil: Abramson, Guillermo. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina;Fil: Semeshenko, Viktoriya. Universidad de Buenos Aires; Argentina;Fil: Iglesias, José Roberto. Universidade Federal Do Rio Grande Do Sul; Brasil

Analyzing mass media influence using natural language processing and time series analysis

A key question of collective social behavior is related to the influence of mass media on public opinion. Different approaches have been developed to address quantitatively this issue, ranging from field experiments to mathematical models. In this work we propose a combination of tools involving natural language processing and time series analysis. We compare selected features of mass media news articles with measurable manifestation of public opinion. We apply our analysis to news articles belonging to the 2016 US presidential campaign. We compare variations in polls (as a proxy of public opinion) with changes in the connotation of the news (sentiment) or in the agenda (topics) of a selected group of media outlets. Our results suggest that the sentiment content by itself is not enough to understand the differences in polls, but the combination of topics coverage and sentiment content provides an useful insight of the context in which public opinion varies. The methodology employed in this work is far general and can be easily extended to other topics of interest.Fil: Albanese, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Pinto, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Semeshenko, Viktoriya. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Interdisciplinario de Economía Política de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Instituto Interdisciplinario de Economía Política de Buenos Aires; ArgentinaFil: Balenzuela, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

Collective states in social systems with interacting learning agents

We consider a social system of interacting heterogeneous agents with learning abilities, a model close to Random Field Ising Models, where the random field corresponds to the idiosyncratic willingness to pay. Given a fixed price, agents decide repeatedly whether to buy or not a unit of a good, so as to maximize their expected utilities. We show that the equilibrium reached by the system depends on the nature of the information agents use to estimate their expected utilities.Comment: 18 pages, 26 figure