This workshop will provide an overview of stochastic modeling approaches for understanding complex social systems, such as agent-based modeling (ABM), network modeling and hybrid modeling approaches for multi-scale systems. Of particular interest will be new simulation techniques, numerical analysis, computational methods and model reduction approaches. Potential focal areas are model derivation and inference for complex social systems, analysis and control of spreading processes, concepts and measurement of transition dynamics and tipping behavior, as well as simulation and model reduction of multi-scale social dynamics. This workshop will be held in combination with the summer school.

The workshop is part of the Thematic Einstein Semester “The Mathematics of Complex Social Systems: Past, Present, and Future”.

**Organizational detail**

**Registration**

Registration is free of charge. To register for this workshop please use the link:

https://www.conftool.net/tes-summer-2022/

Deadline for registration: May 28, 2022

We welcome submissions for posters on the topic of Workshop III “Stochastic modeling of complex social systems”. Submissions should summarize the work to be presented on max. one pdf page including a descriptive figure and references. Please indicate in your submission if you intend to present in person or remotely. The PDF file with your abstract can be uploaded in the registration platform for the event by April 30st, 2022.

**MATH+ organizers**

Nataša Djurdjevac Conrad (ZIB), Stefanie Winkelmann (ZIB), Sarah Wolf (FU/GCF)

**Invited Speakers
**

Robert Axtell (George Mason University)

Sven Banisch (Max-Planck-Institut für Mathematik in den Naturwissenschaften)

Anne Kandler (MPI Leipzig)

Christian Kühn (TU München)

Renaud Lambiotte (University of Oxford)

Jan Nagler (Frankfurt School of Finance and Management)

Iza Romanowska (Aarhus University)

Frank Schweitzer (ETH Zürich)

**Program**

The workshop takes place as a hybrid event, where the on-site part will be at Zuse Institute Berlin in Berlin-Dahlem.

** Tuesday, June 7, 2022:**

9:00-9:30 | Opening | |

9:30-10:30 | Frank Schweitzer | Networks, agents, model selection: Quantifying the social dimension of citation behavior |

10:30-11:00 | Coffee break | |

11:00-12:00 | Jan Nagler | Impact of network motifs on collective response to perturbations |

12:00-13:30 | Lunch break | |

13:30-14:30 | Renaud Lambiotte | Consensus dynamics on temporal hypergraphs |

14:30-15:30 | Sven Banisch | Validating argument-based opinion dynamics with survey experiments |

15:30-16:00 | Coffee break | |

16:00-16:30 | Niklas Wulkow | Data-based modelling of aggregated ABM-variables using memory |

16:30-17:00 | Jan-Hendrik Niemann | Data-driven model reduction of agent-based systems |

17:00-17:30 | MATH+ short talks | |

Marvin Lücke | Concentration effects in the large population limit of the noisy voter model | |

Johannes Zonker | Agent-based modeling of hunter-gatherer societies and their cultural evolution | |

Gesine Steudle | Towards a framework for decision theatre models | |

17:30-19:00 | Poster session |

**Wednesday, June 8, 2022:**

9:00-10:00 | Anne Kandler | From patterns to process in cultural evolution |

10:00-11:00 | Iza Romanowska | ABM as a tool for interdisciplinary research |

11:00-11:30 | Coffee break | |

11:30-12:00 | Natasa Conrad | Mathematics for agent-based models in complex social systems |

12:00-12:30 | Stefanie Winkelmann | Model reduction for metastable population dynamics |

12:30-14:00 | Lunch break | |

14:00-15:00 | Rob Axtell | Emergence and downward causation in agent-based models: Beginnings of a mathematical theory |

15:00-16:00 | Christian Kühn | Adaptive and polyadic network dynamics |

**Content**

Robert Axtell (George Mason University): **Emergence and Downward Causation in Agent-Based Models: Beginnings of a Mathematical Theory**

Agent-based models in the social sciences (and multi-agent systems in computer science) are always multi-level systems, with the behavior of interacting individual agents leading to patterns and regularities at the social (aggregate) level, with intermediate or mesa-level phenomena also often manifesting themselves. When such a system has a certain set of properties, P, at one level that are different from the properties at another level, P’, then it is sometimes useful to characterize the difference in properties as emergent. Such property differences can be either ‘bugs’ or ‘features’ depending on their exact nature. Sometimes such emergence is considered a key model result, especially in the social sciences, such as in the Schelling household location model in which a high-level of segregation emerges despite the individuals having weak preferences to be near people of their own type. Other times, emergence is considered problematical, as when a multi-agent system in computer science is designed to solve some particular problem and unexpected or novel behavior of the system at some level may lead to poor performance overall; in such cases it is common to try to tune such emergence out of a system. Relatedly, philosophers have long debated the extent to which structures and processes that emerge from lower-level components can exert downward causation on the very components that give rise to them in the first place. In this talk I shall attempt to systematize all of these matters by interpreting agent-based models and multi-agent systems in terms of multi-level dynamical systems. The main ideas will be illustrated with an agent-based model of firm dynamics, in which there is constant firm formation, evolution, and exit, yet at the aggregate level realistic numbers and sizes of firms arise. A clear notion of downward causation arises in this work.

Sven Banisch (Max-Planck-Institut für Mathematik in den Naturwissenschaften): **Validating argument-based opinion dynamics with survey experiments**

We combine experimental research on the biased processing of arguments with a computational theory of collective opinion dynamics. While the biased processing of arguments has been frequently reported in social-psychological literature, its integration into argument-based models of opinion dynamics has been missing. In this paper we operationalize the argument communication process employed in these models in conjunction with an experimental design developed to measure biased processing and the resulting attitude changes in the context of energy production technologies. This allows us to analytically compute the expected attitude change through exposure to an unbiased set of arguments for different strengths of biased processing. Calibrating the microlevel assumptions with the experimental data shows a clear signature of moderate biased processing. We further extend the model by incorporating an unbiased external information source providing random arguments at a certain rate (as opposed to receiving arguments from others). The macroscopic opinion distributions emerging from this at the collective level are one-sided clearly in favor (green) or against (coal) a technology and match the surveyed attitudes if we control for the impact of social influence. Sociological model-building reveals that the relationship between biased processing and attitude polarization is not as direct as typical assumed in the psychological literature. The proposed theory generates a series of specific hypotheses that can be tested in future experiments, most notably, it predicts that the impact of biased processing should be stronger on thematic issues on which the population is bi-polarized.

Anne Kandler (MPI Leipzig): **From patterns to process in cultural evolution**

Applying mathematical frameworks describing the dynamics of (cultural) evolutionary processes to real-world data in order to understand the underlying mechanism that – potentially – produced them is an interesting inferential challenge. On the one hand, problems may arise due to characteristics of the available data such as its level of aggregation (e.g., population-level or individual-level data), its sparsity or its spatial and/or temporal resolution. On the other hand, problems may also arise due to misspecifications of the mathematical framework used to analyse the data, e.g., due to the omittance of crucial properties of the cultural system that are able to affect the observed data.

In this talk we discuss these problems by focusing on one the main inverse problems in cultural evolution, namely the inference of processes of social learning form population-level frequency data. In the first part we focus on the coarse distinction between unbiased and biased social learning. We show that in a number of circumstances population-level frequency patterns generated by an unbiased learning (or drift) process may not conform to neutral expectations solely due to unmodelled properties of the cultural system. In more detail, we show that using statistics established in the literature but blind to (i) demographic characteristics of the population such as its age structure or (ii) details of the learning process such as the learning of packages of cultural variants *vs*. the learning of single variants may generate misleading inference results. Further, we demonstrate that the quality of the data, in particular their completeness, can be of crucial importance. The presence, or absence, of rare variants as well as the spread behaviour of innovations may carry a stronger signature about underlying processes than the dynamic of high-frequency variants and the consistency between empirical data and hypotheses about social learning processes can depend entirely on the completeness of the data set.

To address these issues, we advocate in the second part the use of the generative inference approach. This approach allows for the inclusion of – potentially complex – demographic and cultural properties of the cultural system and provides a way to simultaneously evaluate the consistency of a number of learning hypotheses (as opposed to `only’ distinguishing between unbiased and biased social learning) with the available data. This approach consists of a generative mathematical model that establishes a causal link between learning processes and observable frequency data that then are evaluated for statistical consistency. Besides identifying the most likely learning process given the data, this framework determines the breadth of processes that could have produced these data equally well, which in turn allows us to quantify the level of equifinality of the inverse problem and to evaluate the limits of inferring social learning processes from population-level data.

Christian Kühn (TU München): **Adaptive and Polyadic Network Dynamics**

In my talk, I shall provide an update on two aspects that are crucial for modelling complex social systems: (1) new dynamical effects that we discovered in concrete applications such as voter dynamics and epidemic dynamics on networks, and (2) new mathematical tools that we have developed to tackle the increasingly complex models. In particular, I am going to focus on progress for adaptive/co-evolutionary networks, where we have derived mean-field and continuum limit differential equations rigorously and on hypergraph/polyadic interactions, where we have improved numerical algorithms as well as bifurcation-theoretic tools.

Renaud Lambiotte (University of Oxford): **Consensus dynamics on temporal hypergraphs**

We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multiway interactions. We compare these consensus processes with dynamics evolving on projections that remove the temporal and/or the multiway interactions of the higher-order network representation. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multiway interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular, we observe a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, then the majority in these first-mover groups has a higher influence on the final consensus value—a behavior that is not observable in this form in projections of the temporal hypergraph.

Jan Nagler (Frankfurt School of Finance and Management): **Impact of network motifs on collective response to perturbations**

Many collective phenomena such as epidemic spreading and cascading failures in socio-economic systems on networks are caused by perturbations of the dynamics. How perturbations propagate through networks, impact and disrupt their function may depend on the network, the type and location of the perturbation as well as the spreading dynamics. Previous work has analyzed the effects that nodes along propagation paths induce, suggesting few transient propagation scaling regimes as a function of the nodes’ degree, but regardless of motifs such as triangles. Yet, empirical networks consist of motifs enabling the proper functioning of the system. Here, we show that motifs along the propagation path may jointly determine the previously proposed regimes of distance-limited propagation and degree-limited propagation, or even cease their existence. Our analysis suggests not only a radical departure from these scaling regimes but provides a deeper understanding of the interplay of self-dynamics, interaction dynamics, and topological properties.

Iza Romanowska (Aarhus University): **ABM as a tool for interdisciplinary research**

A major, yet often overlooked, advantage of using formal modelling tools is their ability to bring together evidence, data, theory and intuitions from across several scientific disciplines. In this function, ABM can serve as a communication framework between researchers working on the same research problem but from different disciplinary perspectives. Here, I will showcase three case studies where ABM was used to breach the disciplinary boundaries between archaeology and i. Linguistics, ii. Economy and 3. Engineering (robotics). I will argue that ABM has a particular advantage over other types of formal modelling methods due to the more intuitive description of the studied system and the close relation between the modelled entities and everyday experience.

Frank Schweitzer (ETH Zürich): **Networks, agents, model selection: Quantifying the social dimension of citation behavior**

Collaboration networks of scientists are a prime example of complex social systems. We study co-authorship networks to quantify the impact of social constituents, e.g. of previous co-authors, joint publications, on the success of publications as measured by their number of citations. This requires to solve different problems which are addressed in the talk: (i) to model growing networks with two coupled layers, the network of authors and the network of publications, (ii) to generate and test different hypotheses about the coupling between these two layers, (iii) to estimate parameters and compare models with different complexity. But it is worth the effort: After all, producing academic publications is a social endeavour, and our results shed more light on social feedback mechanisms and successful career paths of authors.