arXiv subjects

Eckehard Olbrich

Publications and source records attributed to Eckehard Olbrich.

At least 19 recordsLinked to original sources

arXiv2025

How Influencers and Multipliers Drive Polarization and Issue Alignment on Twitter/X

We investigate the polarization of the German Twittersphere by extracting the main issues discussed and the signaled opinions of users towards those issues based on (re)tweets concerning trending topics. The dataset covers daily trending topics from March 2021 to July 2023. At the opinion level, we show that the online public sphere is largely divided into two camps, one consisting mainly of left-leaning, and another of right-leaning accounts. Further we observe that political issues are strongly aligned, contrary to what one may expect from surveys. This alignment is driven by two cores of strongly active users: influencers, who generate ideologically charged content, and multipliers, who facilitate the spread of this content. The latter are specific to social media and play a crucial role as intermediaries on the platform by curating and amplifying very specific types of content that match their ideological position, resulting in the overall observation of a strongly polarized public sphere. These results contribute to a better understanding of the mechanisms that shape online public opinion, and have implications for the regulation of platforms.

cs.SI↗

arXiv2024

A dynamical model of platform choice and online segregation

In order to truly understand how social media might shape online discourses or contribute to societal polarization, we need refined models of platform choice, that is: models that help us understand why users prefer one social media platform over another. This study develops a dynamic model of platform selection, extending Social Feedback Theory by incorporating multi-agent reinforcement learning to capture how user decisions are shaped by past rewards across different platforms. A key parameter ($\mu$) in the model governs users' tendencies to either seek approval from like-minded peers or engage with opposing views. Our findings reveal that online environments can evolve into suboptimal states characterized by polarized, strongly opinionated echo chambers, even when users prefer diverse perspectives. Interestingly, this polarizing state coexists with another equilibrium, where users gravitate toward a single dominant platform, marginalizing other platforms into extremity. Using agent-based simulations and dynamical systems analysis, our model underscores the complex interplay of user preferences and platform dynamics, offering insights into how digital spaces might be better managed to foster diverse discourse.

nlin.AO↗

arXiv2023

Quantifying synergy and redundancy in multiplex networks

Understanding how different networks relate to each other is key for obtaining a greater insight into complex systems. Here, we introduce an intuitive yet powerful framework to characterise the relationship between two networks comprising the same nodes. We showcase our framework by decomposing the shortest paths between nodes as being contributed uniquely by one or the other source network, or redundantly by either, or synergistically by the two together. Our approach takes into account the networks' full topology, and it also provides insights at multiple levels of resolution: from global statistics, to individual paths of different length. We show that this approach is widely applicable, from brains to the London public transport system. In humans and across 123 other mammalian species, we demonstrate that reliance on unique contributions by long-range white matter fibers is a conserved feature of mammalian structural brain networks. Across species, we also find that efficient communication relies on significantly greater synergy between long-range and short-range fibers than expected by chance, and significantly less redundancy. Our framework may find applications to help decide how to trade-off different desiderata when designing network systems, or to evaluate their relative presence in existing systems, whether biological or artificial.

cs.SI↗

arXiv2023

Continuity and Additivity Properties of Information Decompositions

Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been proposed that such a decomposition should satisfy, leading to different candidate solutions. Curiously, however, only two of the original requirements that determined the Shannon information have been considered, namely monotonicity and normalization. Two other important properties, continuity and additivity, have not been considered. In this contribution, we focus on the mutual information of two finite variables $Y,Z$ about a third finite variable $S$ and check which of the decompositions satisfy these two properties. While most of them satisfy continuity, only one of them is both continuous and additive.

cs.IT↗

arXiv2023

Order-disorder transition in the zero-temperature Ising model on random graphs

The zero-temperature Ising model is known to reach a fully ordered ground state in sufficiently dense random graphs. In sparse random graphs, the dynamics gets absorbed in disordered local minima at magnetization close to zero. Here, we find that the non-equilibrium transition between the ordered and the disordered regime occurs at an average degree that slowly grows with the graph size. The system shows bistability: The distribution of the absolute magnetization in the reached absorbing state is bimodal, with peaks only at zero and unity. For a fixed system size, the average time to absorption behaves nonmonotonically as a function of average degree. The peak value of the average absorption time grows as a power law of the system size. These findings have relevance for community detection, opinion dynamics, and games on networks.

physics.soc-ph↗

arXiv2022

The rise of populism and the reconfiguration of the German political space

The paper explores the notion of a reconfiguration of political space in the context of the rise of populism and its effects on the political system. We focus on Germany and the appearance of the new right wing party "Alternative for Germany" (AfD). Many scholars of politics discuss the rise of the new populism in Western Europe and the US with respect to a new political cleavage related to globalization, which is assumed to mainly affect the cultural dimension of the political space. As such, it might replace the older economic cleavage based on class divisions in defining the dominant dimension of political conflict. An explanation along these lines suggests a reconfiguration of the political space in the sense that (1) the main cleavage within the political space changes its direction from the economic axis towards the cultural axis, but (2) also the semantics of the cultural axis itself is changing towards globalization related topics. Using the electoral manifestos from the Manifesto project database, we empirically address this reconfiguration of the political space by comparing political spaces for Germany built using topic modeling with the spaces based on the content analysis of the Manifesto project and the corresponding categories of political goals. We find that both spaces have a similar structure and that the AfD appears on a new dimension. In order to characterize this new dimension we employ a novel technique, inter-issue consistency networks (IICN) that allow to analyze the evolution of the correlations between the political positions on different issues over several elections. We find that the new dimension introduced by the AfD can be related to the split off of a new "cultural right" issue bundle from the previously existing center-right bundle.

physics.soc-ph↗

arXiv2021

Grounding force-directed network layouts with latent space models

Force-directed layout algorithms are ubiquitously-used tools for network visualisation across a multitude of scientific disciplines. However, they lack theoretical grounding which allows to interpret their outcomes rigorously and can guide the choice of specific algorithms for certain data sets. We propose an approach building on latent space models, which assume that the probability of nodes forming a tie depends on their distance in an unobserved latent space. From such latent space models, we derive force equations for a force-directed layout algorithm. Since the forces infer positions which maximise the likelihood of the given network under the latent space model, the force-directed layout becomes interpretable. We implement these forces for unweighted and weighted networks and spatialise different real-world networks. Comparison to existing layout algorithms (not grounded in an interpretable model) reveals that node groups are placed in similar configurations, while said algorithms show a stronger intra-cluster separation of nodes, as well as a tendency to separate clusters more strongly in retweet networks. We also explore the possibility of visualising data traditionally not seen as network data, such as survey data.

cs.SI↗

arXiv2021

The Twitter Explorer: a Framework for Observing Twitter through Interactive Networks

We present an open-source interface for scientists to explore Twitter data through interactive network visualizations. Combining data collection, transformation and visualization in one easily accessible framework, the twitter explorer connects distant and close reading of Twitter data through the interactive exploration of interaction networks and semantic networks. By lowering the technological barriers of data-driven research, it aims to attract researchers from various disciplinary backgrounds and facilitates new perspectives in the thriving field of computational social science.

cs.SI↗

arXiv2021

Ideological differences in engagement in public debate on Twitter

This article analyses public debate on Twitter via network representations of retweets and replies. We argue that tweets observable on Twitter have both a direct and mediated effect on the perception of public opinion. Through the interplay of the two networks, it is possible to identify potentially misleading representations of public opinion on the platform. The method is employed to observe public debate about two events: The Saxon state elections and violent riots in the city of Leipzig in 2019. We show that in both cases, (i) different opinion groups exhibit different propensities to get involved in debate, and therefore have unequal impact on public opinion. Users retweeting far-right parties and politicians are significantly more active, hence their positions are disproportionately visible. (ii) Said users act significantly more confrontational in the sense that they reply mostly to users from different groups, while the contrary is not the case.

cs.SI↗

arXiv2020

How social feedback processing in the brain shapes collective opinion processes in the era of social media

What are the mechanisms by which groups with certain opinions gain public voice and force others holding a different view into silence? And how does social media play into this? Drawing on recent neuro-scientific insights into the processing of social feedback, we develop a theoretical model that allows to address these questions. The model captures phenomena described by spiral of silence theory of public opinion, provides a mechanism-based foundation for it, and allows in this way more general insight into how different group structures relate to different regimes of collective opinion expression. Even strong majorities can be forced into silence if a minority acts as a cohesive whole. The proposed framework of social feedback theory (SFT) highlights the need for sociological theorising to understand the societal-level implications of findings in social and cognitive neuroscience.

physics.soc-ph↗

arXiv2020

The dynamics of opinion expression

Modelling efforts in opinion dynamics have to a large extent ignored that opinion exchange between individuals can also have an effect on how willing they are to express their opinion publicly. Here, we introduce a model of public opinion expression. Two groups of agents with different opinion on an issue interact with each other, changing the willingness to express their opinion according to whether they perceive themselves as part of the majority or minority opinion. We formulate the model as a multi-group majority game and investigate the Nash equilibria. We also provide a dynamical systems perspective: Using the reinforcement learning algorithm of $Q$-learning, we reduce the $N$-agent system in a mean-field approach to two dimensions which represent the two opinion groups. This two-dimensional system is analyzed in a comprehensive bifurcation analysis of its parameters. The model identifies social-structural conditions for public opinion predominance of different groups. Among other findings, we show under which circumstances a minority can dominate public discourse.

physics.soc-ph↗

arXiv2019

Unique Informations and Deficiencies

Given two channels that convey information about the same random variable, we introduce two measures of the unique information of one channel with respect to the other. The two quantities are based on the notion of generalized weighted Le Cam deficiencies and differ on whether one channel can approximate the other by a randomization at either its input or output. We relate the proposed quantities to an existing measure of unique information which we call the minimum-synergy unique information. We give an operational interpretation of the latter in terms of an upper bound on the one-way secret key rate and discuss the role of the unique informations in the context of nonnegative mutual information decompositions into unique, redundant and synergistic components.

cs.IT↗

arXiv2019

An Argument Communication Model of Polarization and Ideological Alignment

A multi-level model of opinion formation is presented which takes into account that attitudes on different issues are usually not independent. In the model, agents exchange beliefs regarding a series of facts. A cognitive structure of evaluative associations links different (partially overlapping) sets of facts to different political issues and determines an agents' attitudinal positions in a way borrowed from expectancy value theory. If agents preferentially interact with other agents that hold similar attitudes on one or several issues, this leads to biased argument pools and polarization in the sense that groups of agents selectively belief in distinct subsets of facts. Besides the emergence of a bi-modal distribution of opinions on single issues that most previous opinion polarization models address, our model also accounts for the alignment of attitudes across several issues along ideological dimensions.

physics.soc-ph↗

arXiv2019

Unique Information and Secret Key Decompositions

The unique information ($UI$) is an information measure that quantifies a deviation from the Blackwell order. We have recently shown that this quantity is an upper bound on the one-way secret key rate. In this paper, we prove a triangle inequality for the $UI$, which implies that the $UI$ is never greater than one of the best known upper bounds on the two-way secret key rate. We conjecture that the $UI$ lower bounds the two-way rate and discuss implications of the conjecture.

cs.IT↗

arXiv2018

Opinion Polarization by Learning from Social Feedback

We explore a new mechanism to explain polarization phenomena in opinion dynamics in which agents evaluate alternative views on the basis of the social feedback obtained on expressing them. High support of the favored opinion in the social environment, is treated as a positive feedback which reinforces the value associated to this opinion. In connected networks of sufficiently high modularity, different groups of agents can form strong convictions of competing opinions. Linking the social feedback process to standard equilibrium concepts we analytically characterize sufficient conditions for the stability of bi-polarization. While previous models have emphasized the polarization effects of deliberative argument-based communication, our model highlights an affective experience-based route to polarization, without assumptions about negative influence or bounded confidence.

physics.soc-ph↗

arXiv2017

On extractable shared information

We consider the problem of quantifying the information shared by a pair of random variables $X_{1},X_{2}$ about another variable $S$. We propose a new measure of shared information, called extractable shared information, that is left monotonic; that is, the information shared about $S$ is bounded from below by the information shared about $f(S)$ for any function $f$. We show that our measure leads to a new nonnegative decomposition of the mutual information $I(S;X_1X_2)$ into shared, complementary and unique components. We study properties of this decomposition and show that a left monotonic shared information is not compatible with a Blackwell interpretation of unique information. We also discuss whether it is possible to have a decomposition in which both shared and unique information are left monotonic.

cs.IT↗

arXiv2017

Coarse-graining and the Blackwell order

Suppose we have a pair of information channels, $κ_{1},κ_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $κ_{1}$ and $κ_{2}$ by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, $κ_{1}$ is said to be Blackwell-inferior to $κ_{2}$ if and only if $κ_{1}$ can be constructed by garbling the output of $κ_{2}$. A related partial order stipulates that $κ_{2}$ is more capable than $κ_{1}$ if the mutual information between the input and output is larger for $κ_{2}$ than for $κ_{1}$ for any distribution over inputs. A Blackwell-inferior channel is necessarily less capable. However, examples are known where $κ_{1}$ is less capable than $κ_{2}$ but not Blackwell-inferior. We show that this may even happen when $κ_{1}$ is constructed by coarse-graining the inputs of $κ_{2}$. Such a coarse-graining is a special kind of "pre-garbling" of the channel inputs. This example directly establishes that the expected value of the shared utility function for the coarse-grained channel is larger than it is for the non-coarse-grained channel. This contradicts the intuition that coarse-graining can only destroy information and lead to inferior channels. We also discuss our results in the context of information decompositions.

cs.IT↗

arXiv2017

The approach towards equilibrium in a reversible Ising dynamics model -- an information-theoretic analysis based on an exact solution

We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.

cond-mat.stat-mech↗