Polarization in Geometric Opinion Dynamics

Gaitonde, Jason; Kleinberg, Jon; Tardos, Éva

doi:10.1145/3465456.3467633

Cited by 15 publications

(16 citation statements)

References 8 publications

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“…We leave a number of questions for future research. As discussed, recent work on mathematical models of opinion dynamics has sought to understand the impact of outside actors (who can modify the graph 𝐺 is some way) on individual opinions and polarization [3,26]. There is little work on how such modifications impact group-based polarization, and if they can accelerate its emergence.…”

Section: Discussionmentioning

confidence: 99%

“…The unrealistic monotonic dynamics of variance-based measures have led past studies to abandon simple opinion models like the DeGroot dynamics, and to adopt alternative, more complicated models to mathematically recover interesting polarization dynamics. For example, the Friedkin-Johnson dynamics [24], bounded confidence model [45], and geometric models have all seen recent attention [26,32]. A central conclusion of our work is that, alternatively, it may be the definition of polarization, not the model, that lacks richness for understanding societal polarization.…”

Section: Conclusion and Recommendationsmentioning

confidence: 96%

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How to Quantify Polarization in Models of Opinion Dynamics

Musco¹,

Indu²,

Ugander³

et al. 2021

Preprint

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It is widely believed that society is becoming increasingly polarized around important issues, a dynamic that does not align with common mathematical models of opinion formation in social networks. In particular, measures of polarization based on opinion variance are known to decrease over time in frameworks such as the popular DeGroot model. Complementing recent work that seeks to resolve this apparent inconsistency by modifying opinion models, we instead resolve the inconsistency by proposing changes to how polarization is quantified.We present a natural class of group-based polarization measures that capture the extent to which opinions are clustered into distinct groups. Using theoretical arguments and empirical evidence, we show that these group-based measures display interesting, nonmonotonic dynamics, even in the simple DeGroot model. In particular, for many natural social networks, group-based metrics can increase over time, and thereby correctly capture perceptions of increasing polarization.Our results build on work by DeMarzo et al., who introduced a group-based polarization metric based on ideological alignment. We show that a central tool from that work, a limit analysis of individual opinions under the DeGroot model, can be extended to the dynamics of other group-based polarization measures, including established statistical measures like bimodality.We also consider local measures of polarization that operationalize how polarization is perceived in a network setting. In conjunction with evidence from prior work that group-based measures better align with real-world perceptions of polarization, our work provides formal support for the use of these measures in place of variance-based polarization in future studies of opinion dynamics. CCS CONCEPTS• Human-centered computing → Social networks; • Theory of computation → Social networks.

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Section: Discussionmentioning

confidence: 99%

Section: Conclusion and Recommendationsmentioning

confidence: 96%

How to Quantify Polarization in Models of Opinion Dynamics

Musco¹,

Indu²,

Ugander³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In the real world, the phenomenon of polarization among agents are attracting increasing attention [26]. In this section, we consider a polarized opinion scenario in which, the neighborhood radius is set to 2 such that agents are unable to reach agreement without controls.…”

Section: B Consensus In the Phenomenon Of Polarizationmentioning

confidence: 99%

Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control

Chen¹,

Wang²,

Theodorou³

2022

Preprint

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In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probabilistic representation of the solution of the Hamilton-Jacobi-Bellman partial differential equation. Grounded on the nonlinear version of the Feynman-Kac lemma, the solutions of the Hamilton-Jacobi-Bellman partial differential equation are linked to the solution of a set of Forward-Backward Stochastic Differential Equations. These equations can be solved numerically using a novel deep neural network with architecture tailored to the problem in consideration. The resulting algorithm is tested on a polarized opinion consensus experiment. We showcase the scalability and generalizability of our algorithm on a 10k agent experiment. The proposed framework opens up the possibility for future applications on extremely large-scale problems.

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“…They show that even when content is chosen uniformly at random, the biased assimilation dynamics result in a polarized population almost surely on an infinite horizon. Gaitonde et al [2021] consider a broader class of opinion dynamics in this non-personalized setting and develop a more nuanced analysis of the polarization phenomena on infinite time horizons.…”

Section: Opinion and Preference Dynamicsmentioning

confidence: 99%

“…Motivated by these effects of content providers on user beliefs or preferences, recent work has aimed to understand in what contexts non-personalized content recommendation can lead to polarization [Hązła et al, 2019, Gaitonde et al, 2021. The models capture biased assimilation, assuming individuals whose beliefs initially align with content they observe will update their beliefs to align more closely with that content, while individuals who disagree with content they see will disagree more strongly after seeing that content.…”

Section: Introductionmentioning

confidence: 99%

Preference Dynamics Under Personalized Recommendations

Dean¹,

Morgenstern²

2022

Preprint

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The design of content recommendation systems underpins many online platforms: social media feeds, online news aggregators, and audio/video hosting websites all choose how best to organize an enormous amount of content for users to consume. Many projects (both practical and academic) have designed algorithms to match users to content they will enjoy under the assumption that user's preferences and opinions do not change with the content they see.However, increasing amounts of evidence suggest that individuals' preferences are directly shaped by what content they see-radicalization, rabbit holes, polarization, and boredom are all example phenomena of preferences affected by content. Polarization in particular can occur even in ecosystems with "mass media," where no personalization takes place, as recently explored in a natural model of preference dynamics by Hązła et al. [2019] and Gaitonde et al. [2021]. If all users' preferences are drawn towards content they already like, or are repelled from content they already dislike, uniform consumption of media leads to a population of heterogeneous preferences converging towards only two poles.In this work, we explore whether some phenomenon akin to polarization occurs when users receive personalized content recommendations. We use a similar model of preference dynamics, where an individual's preferences move towards content the consume and enjoy, and away from content they consume and dislike. We show that standard user reward maximization is an almost trivial goal in such an environment (a large class of simple algorithms will achieve only constant regret). A more interesting objective, then, is to understand under what conditions a recommendation algorithm can ensure stationarity of user's preferences. We show how to design a content recommendations which can achieve approximate stationarity, under mild conditions on the set of available content, when a user's preferences are known, and how one can learn enough about a user's preferences to implement such a strategy even when user preferences are initially unknown.

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Polarization in Geometric Opinion Dynamics

Cited by 15 publications

References 8 publications

How to Quantify Polarization in Models of Opinion Dynamics

How to Quantify Polarization in Models of Opinion Dynamics

Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control

Preference Dynamics Under Personalized Recommendations

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