We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards an average opinion, whereas low thresholds result in several opinion clusters: members of the same cluster share the same opinion but are no longer influenced by members of other clusters.

We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions toward an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalized to network interactions

Abstract:In , 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 di erences 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 o en in interactions, social influence reduces di erences 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 su ers 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 e ects of social media on societal polarization.

Abstract. The increasing integration of technology into our lives has created unprecedented volumes of data on society's everyday behaviour. Such data opens up exciting new opportunities to work towards a quantitative understanding of our complex social systems, within the realms of a new discipline known as Computational Social Science. Against a background of financial crises, riots and international epidemics, the urgent need for a greater comprehension of the complexity of our interconnected global society and an ability to apply such insights in policy decisions is clear. This manifesto outlines the objectives of this new scientific direction, considering the challenges involved in it, and the extensive impact on science, technology and society that the success of this endeavour is likely to bring about.

We propose a new approximate Bayesian computation (ABC) algorithm that aims at minimizing the number of model runs for reaching a given quality of the posterior approximation. This algorithm automatically determines its sequence of tolerance levels and makes use of an easily interpretable stopping criterion. Moreover, it avoids the problem of particle duplication found when using a MCMC kernel. When applied to a toy example and to a complex social model, our algorithm is 2 to 8 times faster than the three main sequential ABC algorithms currently available. Sequential Monte-Carlo methods in approximate Bayesian computationIn this section we present the three main sequential ABC algorithms currently available and their limitations. We present the Population Monte-Carlo ABC proposed in [10] (hereafter called PMC), the Replenishment Sequential Monte-Carlo ABC proposed in [12] and the Sequential Monte-Carlo ABC proposed in [13]. These algorithms are detailed in Appendix A.