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

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

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

Entanglement between Demand and Supply in Markets with Bandwagon Goods

Whenever customers' choices (e.g. to buy or not a given good) depend on others choices (cases coined 'positive externalities' or 'bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one -- in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T C Schelling in the 70's.Comment: Updated version, accepted for publication, Journal of Statistical Physics, online Dec 201

Portrait comparison of binary and weighted Skill Relatedness Networks

In this paper we compare Skill-Relatedness Networks (SRNs) for selected countries, that is to say statistically significant inter-industrial interactions representing latent skills exchanges derived from observed labor flows, a kind of industry spaces. Using data from Argentina (ARG), Germany (DEU) and Sweden (SWE), we compare their SRNs utilizing an information-theoretic method that permits to compare networks of "non-aligned" nodes, which is the case of interest. For each SRN we extract its portrait, a fingerprint of structural measures of the distributions of their shortest paths, and calculate their pairwise divergences. This allows us also to contrast differences in structural (binary) connectivity with differences in the information provided by the (weighted) skill relatedness indicator (SR). We find that, in the case of ARG, structural connectivity is very different from their counterpart in DEU and SWE, but through the glass of SR the distances analyzed are all substantially smaller and more alike. These results qualify the role of the SR indicator as revealing some hidden dimension different from connectivity alone, providing empirical support to the suggestion that industry spaces may differ across countries.In this paper we compare Skill-Relatedness Networks (SRNs) for selected countries, that is to say statistically significant inter-industrial interactions representing latent skills exchanges derived from observed labor flows, a kind of industry spaces. Using data from Argentina (ARG), Germany (DEU) and Sweden (SWE), we compare their SRNs utilizing an information-theoretic method that permits to compare networks of "non-aligned" nodes, which is the case of interest. For each SRN we extract its portrait, a fingerprint of structural measures of the distributions of their shortest paths, and calculate their pairwise divergences. This allows us also to contrast differences in structural (binary) connectivity with differences in the information provided by the (weighted) skill relatedness indicator (SR). We find that, in the case of ARG, structural connectivity is very different from their counterpart in DEU and SWE, but through the glass of SR the distances analyzed are all substantially smaller and more alike. These results qualify the role of the SR indicator as revealing some hidden dimension different from connectivity alone, providing empirical support to the suggestion that industry spaces may differ across countries

Interdependent binary choices under social influence: phase diagram for homogeneous unbiased populations

Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are considered. The nonlocal or group interdependence model is used to study two interrelated groups making the same binary choice. The local or individual interdependence model represents a single group where agents make two binary choices which depend on each other. For both models, phase diagrams, and their implications in socioeconomic contexts, are described and compared in the absence of private deterministic utilities (zero opinion fields).Comment: 17 pages, 3 figures. This is the pre-peer reviewed version of the following article: Ana Fern\'andez del R\'io, Elka Korutcheva and Javier de la Rubia, Interdependent binary choices under social influence, Wiley's Complexity, 2012; which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/cplx.21397/abstrac