Workshop

“Formal Models of Social Networks & Democracy”
February 8-9 2024, Groningen

This workshop is supported by Zoé Christoff’s NWO VENI (2020) research project “Democracy on Social Networks”. The project applies formal tools to model how network structures affect opinion formation and collective decision making. The goal of the workshop is to bring together researchers interested in the impact of (online) social networks on democracy from different backgrounds and perspectives.

Location: The workshop will be held in the city center of Groningen, in the “Stadszaal” room on the first floor of ‘t Feithuis, Martinikerkhof 10, 9712 JG Groningen.

Programme:

Thursday 8 February	Speaker	Title
9:00 – 9:30		Arrival and coffee
9:30 – 9:45	Zoé Christoff	Introduction
9:45 – 10:30	Thomas Ågotnes	Common-Enough Knowledge and The Collective Action Problem in Social Networks
10:30 – 11:00		Coffee break
11:00 – 11:45	Nina Gierasimczuk	Unboxing learning processes with dynamic modal logics
11:45 – 12:30	Edoardo Baccini	Comparing Social Network Dynamics
12:30 – 14:00		Lunch break
14:00 – 14:45	Mina Young Perdersen	Detecting Bots with Temporal Logic
14:45 – 15:30	Maaike Venema-Los	On the graph theory of majority illusions
15:30 – 16:00		Coffee break
16:00 – 16:45	Larry Moss	Majority rules
18:00		Workshop Dinner Osteria da Vinci

Friday 9 February	Speaker	Title
9:15 – 10:00	Jan-Willem Romeijn	Extremizing: Social learning meets meta-analysis
10:00 – 10:45	Hendrik Siebe	The interdependence of social deliberation and judgment aggregation
10:45 – 11:15		Coffee break
11:15 – 12:00	Sonja Smets	Logic and Computation of Social Behavior
12:00- 13:30		Lunch break
13:30 – 14:15	Dominik Klein	Hegselmann-Krause studied through the lense of judgment aggregation
14:15 – 15:00	Ines Lindner	Naïve Learning in Social Networks: Bots as a Singularity
15:00 – 15:30		Coffee break
15:30 – 16:15	Davide Grossi	Condorcet Markets

Abstracts:

– Thomas Ågotnes (University of Bergen) – Common-Enough Knowledge and The Collective Action Problem in Social Networks:
We consider the collective action problem in social networks: the problem of coordinated joint action in a social network, where each agent who participates gets a benefit if and only if enough agent participate, and possibly severe punishment if not. There are both similarities and differences to informational cascades: agents might have individual thresholds, but they have to coordinate and act simultaneously — they can’t wait and see what their friends do. Knowledge is central here: there might be a majority group without anyone in that group knowing that they are member of a majority and thus choose not to participate. Models explaining the effect of knowledge on collective action in social networks, such as those suggested by Michael Chwe and collagues, typically make assumptions about the relationship between the network structure and agents’ knowledge (e.g., that you only know the thresholds of your immediate friends but that you know the complete friendship relation). The epistemic aspect here is not only central but also non-trivial. By a similar argument to the above, it might be that everyone in the majority groups knows that they are in a majority group, without knowing that the others know. It has therefore been argued that common knowledge (in the group) of the fact that a group decides to participate, is necessary for the group members to participate. In this work we argue that that is actually not always the case, sometimes a weaker notion of group knowledge is sufficient. We call that common-enough knowledge. The talk is based on joint work with Zoé Christoff.

– Edoardo Baccini (University of Groningen) – Comparing Social Network Dynamics:
Joint work with Zoé Christoff and Rineke Verbrugge.
In this talk, we present a comprehensive logical framework to reason about threshold-driven diffusion and threshold-driven link change in social networks. We consider both monotonic dynamics, where agents can only adopt new features and create new connections, and non-monotonic dynamics, where agents may also abandon features or cut ties. Three types of operators are combined: one capturing diffusion only, one capturing link change only, and one capturing both at the same time. We first show that our operators (and any combination of them) are irreplaceable, in the sense that the sequences of model updates expressed by a combination of operators cannot always be expressed using any other operators. We then turn to study some classes of models on which some operators can be replaced.

– Nina Gierasimczuk (DTU Compute) – Unboxing learning processes with dynamic modal logics:
At present, the field of Artificial Intelligence is split between two paradigms: symbolic reasoning (relying on computational logic) and connectionist learning (embodied in neural systems). Among many important issues is that of explainability: How can we unpack the black-box processes of learning? There are at least three different perspectives on learning that allow a dynamic modal logic approach: learning as transitioning between nodes in a graph of hypotheses, learning as taking advantage of observations in epistemic and topological spaces, and, finally, learning as propagation in a (neural) network. In this talk, I will overview and compare these approaches, and I will evaluate their importance for the question of explainability in AI.

– Davide Grossi (University of Groningen and University of Amsterdam) – Condorcet Markets:
In this talk I will present on-going work on establishing formal relationships between weighted majority elections and information markets in a binary truth-tracking setting. I will present correspondence results showing how weighted majority elections and specific classes of information markets implement the same collective truth-tracking behaviour. The aim is to provide common foundations to both elections and information markets in the framework of epistemic social choice. 
Joint work with Nicholas Kees Dupuis and Stéphane Airiau.

– Dominik Klein (University of Utrecht) – Hegselmann-Krause studied through the lense of judgment aggregation:
In this talk, we’ll analyze opinion dynamics in a Hegselmann Krause model through two lenses. Firstly, we consider Hegselmann Krause dynamics to consensus (whenever it results) as a case of judgment aggregation. We analyze how the process fares with respect to a number of standard axioms in judgment aggregation. Secondly, we analyze how complexly the consensus value relates to changes in the individual input conditions, e.g. when all individuals move their opinions towards the same direction. This is joint work with Hein Duijf.

– Ines Lindner (Vrije Universiteit Amsterdam) – Naïve Learning in Social Networks: Bots as a
Singularity:
We study the impact of bots on social learning in a social network setting. Regular agents receive independent noisy signals about the true value of a variable and then communicate in a network. They naïvely update beliefs by repeatedly taking weighted averages of neighbors’ opinions. Bots are agents in the network that spread fake news by disseminating biased information. Our main contributions are threefold. (1) We show that the consensus of the network is a mapping of the interaction rate between the agents and bots and is discontinuous at zero mass of bots. This implies that even a comparatively “infinitesimal” small number of bots still has a sizeable impact on the consensus and hence represents an obstruction to the “wisdom of crowds”. (2) We prove that the consensus gap induced by the marginal presence of bots depends neither on the agent network or bot layout nor on the assumed connection structure between agents and bots. (3) We show that before the ultimate (and bot-infected) consensus is reached, the network passes through a quasi-stationary phase which has the potential to mitigate the harmful impact of bots.
This is joint work with Saeed Badria and Bernd Heidergottb.

– Larry Moss (Indiana University) – Majority rules:
Democracy means many things.  Arguably, ‘majority rule’ is one of them.  Even before we add in network models, there is the prior task of reasoning about settings where ‘majority’ behavior is at issue.  This talk aims at simple forms of logic which have sentences ‘most x are y’, with the meaning “there are more x’s which are y’s than x’s which are not y’s.” Of course one wants to add other sentences as well.  For example, one might like to some or all of the sentence forms of syllogistic logic, or to take boolean combinations of the variables x and y.  There are a few complete logical systems to discuss, and also some remaining open problems.  I also will try to connect the purely logical work to matters closer to the themes of the conference. 

– Jan-Willem Romeijn (University of Groningen) – Extremizing: Social learning meets meta-analysis:
Joint work with Simon Huttegger (UC Irvine). Our paper is concerned with methods of aggregating statistical results. The direct motivation is a phenomenon known as “extremizing”: in some cases it seems rational to bring the aggregated opinion beyond all the individual expert opinions, i.e., q* >  qi for all experts i. This phenomenon can be connected to the “risky shift” observed in social psychology, where agents irrationally amplify each others’ opinions. But it also naturally relates to successful forecasting methods, as discussed in Tetlock’s popular science book “Superforecasters”, and to corrections on the biases described in Kahneman’s prospect theory. We present three Bayesian models of increasing complexity in which extremizing can be explained and motivated. They offer insights by which we can connect themes from inductive logic, social learning, and statistical meta-analysis.

– Hendrik Siebe (University of Groningen) –  The interdependence of social deliberation and judgment aggregation:
An epistemic goal of social deliberation is to improve the competence of the participants, but does this also create a wiser crowd? In this talk I present two models that show individual and social epistemology coming interestingly apart. This phenomenon of “tragic competence-raising” implies that our normative reflection on the presence or nature of social deliberation should take into account how post-deliberative individual judgments are to be aggregated towards group judgments.

– Sonja Smets (University of Amsterdam) –  Logic and Computation of Social Behavior:
Following the recent development in which logical methods can be applied to the formal analysis of social networks, I present work on the use of logic to study social influence and herd behavior in epistemic social networks. In such networks, we first consider agents who adopt a new fashion or behavior depending on whether a “sufficiently large enough group” of their neighbors already has adopted the behavior. We provide different types of models as well as a simple qualitative modal language to reason about the concept of a “strong enough” trigger of influence. Using fixed-point operators in our logic, important results from network theory about the characterization of informational cascades follow immediately from our logical axioms. The results presented in this talk are based on on-going joint work with Alexandru Baltag at the University of Amsterdam.

– Maaike Venema-Los (University of Groningen) – On the Graph Theory of Majority Illusions:
This is joint work with Zoé Christoff and Davide Grossi.
The popularity of an opinion in one’s direct circles is not necessarily a good indicator of its popularity in one’s entire community. For instance, when confronted with a majority of opposing opinions in one’s circles, one might get the impression that one belongs to a minority. From this perspective, network structure makes local information about global properties of the group potentially inaccurate. However, the way a social network is wired also determines what kind of information distortion can actually occur. In this talk, I will discuss which classes of networks allow for large groups of agents to have a wrong impression about the distribution of opinions in the network. We focus on the case where agents are wrong about the majority opinion, that is, they are under ‘majority illusion’, and generalize to other types of illusions. 

– Mina Young Pedersen (University of Bergen) – Detecting bots with temporal logic:
Social bots are computer programs that act like human users on social media. Although social bots may have a beneficial purpose, they are often used to amplify and direct misinformation. In this talk, I will present a project where we propose using model checking as a tool to detect social bots. This entails checking formulas representing bot behavior against social networks represented by logic models. We use temporal logic to follow a social network as it evolves through time, and present two languages to formalize bot behavior. With the first language, we can check whether it is likely that there exist bots in the network. With the second language, we can also check who in the network is likely a bot, but it comes at an expense in terms of model checking complexity. The presentation is based on joint work with Marija Slavkovik and Sonja Smets.