Mathematical models for social group behavior

In this paper, we seek to identity how mathematical and economic analysis can be used to gain insights about the mutation of social groups. Group mutability has been studied in multiple domains, with insights generated on significant factors at differing scales. Mathematical modeling enables the simultaneous study of such phenomena, understanding interactions and generating hypotheses for experiments. In particular, we focus on group fracture, where individuals leave groups of which they are members. For example, this can be due to perceived differences with other group members due to norm related conflict (such as extreme actions by some members). Our aim is to consider simple mathematical models incorporating a selection of social and psychological theory which describes these phenomena as a way to understand their interplay, and describe the trade-offs and challenges. This will help a federation model the behavior of extremist groups, and determine not only when an intervention is necessary, but also the best course of action to take to induce the fracture of such groups. This paper is an exploratory investigation into methods of achieving this goal and evaluating the usefulness of the outputs to federations

Why Are There Descriptive Norms? Because We Looked for Them

In this work, we present a mathematical model for the emergence of descriptive norms, where the individual decision problem is formalized with the standard Bayesian belief revision machinery. Previous work on the emergence of descriptive norms has relied on heuristic modeling. In this paper we show that with a Bayesian model we can provide a more general picture of the emergence of norms, which helps to motivate the assumptions made in heuristic models. In our model, the priors formalize the belief that a certain behavior is a regularity. The evidence is provided by other group members’ behavior and the likelihood by their reliability. We implement the model in a series of computer simulations and examine the group-level outcomes. We claim that domain-general belief revision helps explain why we look for regularities in social life in the first place. We argue that it is the disposition to look for regularities and react to them that generates descriptive norms. In our search for rules, we create them

Mechanisms for Social Influence

Throughout the thesis, I study mathematical models that can help explain the dependency of social phenomena in animals and humans on individual traits. The first chapter investigates consensus building in human groups through communication of individual preferences for a course of action. Individuals share and modify these preferences through speaker listener interactions. Personality traits, reputations, and social networks structures effect these modifications and eventually the group will reach a consensus. If there is variation in personality traits, the time to reach consensus is delayed. Reputation models are introduced and explored, finding that those who can best estimate the average initial preference and who have the best knowledge to what the optimal decision is for the group become the most reputable. If there is one individual, an informal leader, who is stubborn, persuasive, reputable, and socially connected then the time to reach consensus is reduced. The second chapter introduces a model for the emergence of play behavior in animals. An individual-based model is proposed where organisms compete for resources in the environment. Play is introduced as a frivolous behavior that increases energy use and the probability of dying. Simulations show that play behavior becomes fixed in the population and the time spent playing is maintained at a low rate in regardless of its costly nature. When play behavior is directly functional by increasing foraging ability, it evolves quickly and the time individuals spend playing increases, but eventually the population of players collapses and play disappears. Play acts as a spiteful behavior in that playing individuals suffer a direct cost to their fitness, but also results in players consuming more resources incurring a greater cost to other individuals in the population through reduced probability of successfully foraging

Leadership and Teamwork in Innovation Ecosystems

As experts acknowledge innovation is rarely driven by individuals acting in an isolated capacity, it is generally a social and collaborative element that triggers the concepts of organizational behavior. The question is then how to create environments in projects and in organizations where individual’s creativity and contribution fosters pollination to drive innovation. Studies confirm that the key impacting element in this area is teamwork quality, rather than team composition. Thus, organizations need to create teams with key traits that drive positive collaborations such as communication, coordination, balance of member contributions, mutual support, effort, and cohesion. These traits will allow a social group to deal with the inevitable creative tension needed for innovation ecosystems to flourish. Since human behavior is not mathematical, the only way to do this is creating the conditions for these traits to appear. In this context, leaders as social architects become very important, setting the tone of the organization, clearly defining the mission, identifying and living shared values, setting example, and understanding how organizations and social groups behave. When they are able to build high quality and performing environments, they become innovation brokers generating models that are scalable to be able to impact communities

Computational modelling with uncertainty of frequent users of e-commerce in Spain using an age-group dynamic nonlinear model with varying size population

[EN] Electronic commerce (EC) has numerous advantages. It allows saving time when we purchase an item, offers the possibility of review without depending on the schedules of traditional stores, access to a wider variety and quantity of articles, in many cases, with lower prices, etc. Based upon mathematical epidemiology tenets strongly related to social behavior able to describe the influence of peers, in this paper we propose an age-group dynamic model with population varying size based on a system of difference equations to study the evolution of the frequent users of EC over time in Spain. Using data from surveys retrieved from the Spanish National Statistics Institute, we use and design computational algorithms to perform a probabilistic estimation of the model parameters that allow the model output to capture the data uncertainty. Then, we will be able to perform a precise prediction with uncertainty.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P and by the European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010.Burgos-Simon, C.; Cortés, J.; Martínez-Rodríguez, D.; Villanueva Micó, RJ. (2019). Computational modelling with uncertainty of frequent users of e-commerce in Spain using an age-group dynamic nonlinear model with varying size population. Advances in Complex Systems. 22(4):1950009-1-1950009-17. https://doi.org/10.1142/S0219525919500097S1950009-11950009-17224Bettencourt, L. (1997). Customer voluntary performance: Customers as partners in service delivery. Journal of Retailing, 73(3), 383-406. doi:10.1016/s0022-4359(97)90024-5Brauer, F., & Castillo-Chávez, C. (2001). Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics. doi:10.1007/978-1-4757-3516-1Cortés, J.-C., Lombana, I.-C., & Villanueva, R.-J. (2010). Age-structured mathematical modeling approach to short-term diffusion of electronic commerce in Spain. Mathematical and Computer Modelling, 52(7-8), 1045-1051. doi:10.1016/j.mcm.2010.02.030Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 42(4), 599-653. doi:10.1137/s0036144500371907Yanhui, L., & Siming, Z. (2007). Competitive dynamics of e-commerce web sites. Applied Mathematical Modelling, 31(5), 912-919. doi:10.1016/j.apm.2006.03.029Mahajan, V., Muller, E., & Bass, F. M. (1991). New Product Diffusion Models in Marketing: A Review and Directions for Research. Diffusion of Technologies and Social Behavior, 125-177. doi:10.1007/978-3-662-02700-4_6Turban, E., Outland, J., King, D., Lee, J. K., Liang, T.-P., & Turban, D. C. (2018). Electronic Commerce 2018. Springer Texts in Business and Economics. doi:10.1007/978-3-319-58715-

Ultrametricity increases the predictability of cultural dynamics

A quantitative understanding of societies requires useful combinations of empirical data and mathematical models. Models of cultural dynamics aim at explaining the emergence of culturally homogeneous groups through social influence. Traditionally, the initial cultural traits of individuals are chosen uniformly at random, the emphasis being on characterizing the model outcomes that are independent of these (`annealed') initial conditions. Here, motivated by an increasing interest in forecasting social behavior in the real world, we reverse the point of view and focus on the effect of specific (`quenched') initial conditions, including those obtained from real data, on the final cultural state. We study the predictability, rigorously defined in an information-theoretic sense, of the \emphsocial content of the final cultural groups (i.e. who ends up in which group) from the knowledge of the initial cultural traits. We find that, as compared to random and shuffled initial conditions, the hierarchical ultrametric-like organization of empirical cultural states significantly increases the predictability of the final social content by largely confining cultural convergence within the lower levels of the hierarchy. Moreover, predictability correlates with the compatibility of short-term social coordination and long-term cultural diversity, a property that has been recently found to be strong and robust in empirical data. We also introduce a null model generating initial conditions that retain the ultrametric representation of real data. Using this ultrametric model, predictability is highly enhanced with respect to the random and shuffled cases, confirming the usefulness of the empirical hierarchical organization of culture for forecasting the outcome of social influence models

Invited review: Epidemics on social networks

Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases.In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed.These new models incorporated concepts from graph theory to describe and model the underlying social structure.Many of these works merely produced a more detailed extension of the previous results, but some others triggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basic concepts of epidemiology, epidemic modeling and networks, to finally provide a brief description of the most relevant results in the field.Comment: 17 pages, 13 figure