Modeling confirmation bias and polarization (1607.00022v1)

Abstract: Online users tend to select claims that adhere to their system of beliefs and to ignore dissenting information. Confirmation bias, indeed, plays a pivotal role in viral phenomena. Furthermore, the wide availability of content on the web fosters the aggregation of likeminded people where debates tend to enforce group polarization. Such a configuration might alter the public debate and thus the formation of the public opinion. In this paper we provide a mathematical model to study online social debates and the related polarization dynamics. We assume the basic updating rule of the Bounded Confidence Model (BCM) and we develop two variations a) the Rewire with Bounded Confidence Model (RBCM), in which discordant links are broken until convergence is reached; and b) the Unbounded Confidence Model, under which the interaction among discordant pairs of users is allowed even with a negative feedback, either with the rewiring step (RUCM) or without it (UCM). From numerical simulations we find that the new models (UCM and RUCM), unlike the BCM, are able to explain the coexistence of two stable final opinions, often observed in reality. Lastly, we present a mean field approximation of the newly introduced models.

• The paper extends the Bounded Confidence Model by introducing mechanisms like unbounded confidence (opinion repulsion) and dynamic network rewiring.
• Simulations demonstrate that models incorporating opinion repulsion or network rewiring effectively capture and sustain polarized states with multiple opinion peaks.
• These new models offer valuable insights for understanding online social influence dynamics and inform potential strategies for mitigating extreme polarization on digital platforms.

Modeling Confirmation Bias and Polarization

The paper "Modeling Confirmation Bias and Polarization" by Del Vicario et al. investigates the dynamics of opinion formation and polarization in online networks, focusing on the role of confirmation bias and social influence in creating echo chambers. The authors develop a mathematical framework that extends the Bounded Confidence Model (BCM) to introduce new mechanisms capable of capturing the empirical coexistence of multiple stable opinions.

Mathematical Framework and Models

The authors begin with the Bounded Confidence Model (BCM), which posits that agents update their opinions only when their viewpoints are sufficiently close. The model traditionally leads to consensus or opinion clustering depending on the tolerance parameter $\varepsilon$.

To address the limitations of BCM in explaining the real-world persistence of polarized opinions, three extensions are proposed:

1. Rewire with Bounded Confidence Model (RBCM): Agents can rewire their connections if their opinions are too far apart. This model preserves network topology dynamics while enforcing convergence by progressively eliminating discordant links.
2. Unbounded Confidence Model (UCM): This model allows interaction regardless of initial opinion distance, introducing a repulsive mechanism where discordant interactions push opinions further apart. This reflects the real-world phenomenon of opinion polarization due to negative interactions.
3. Rewire with Unbounded Confidence Model (RUCM): Combining the rewiring feature with the unbounded interaction, this model allows both negative interaction-induced polarization and dynamic network restructuring.

Simulation and Results

The authors perform extensive simulations on Scale-Free networks to evaluate the models' behavior across a range of parameters ($\varepsilon$ and $\mu$, where $\mu$ is the convergence factor). The results demonstrate that:

• BCM and RBCM: Show consensus or clustering into multiple opinion groups contingent on the tolerance parameter.
• UCM and RUCM: Display the coexistence of two prominent opinions across broad parameter regions, effectively capturing polarized states often observed in real-world networks.

A significant finding is the enhanced role of the $\mu$ parameter in UCM and RUCM, which influences the rate of convergence and interaction outcomes, highlighting the adaptability of opinion landscapes based on individual interaction dynamics.

Conclusion and Implications

The introduction of these models provides a significant step forward in modeling social influence and polarization by incorporating mechanisms observed in digital communication platforms. The capability of UCM and RUCM to sustain multiple opinion peaks aligns well with empirical observations of polarized online communities.

From both a theoretical and practical perspective, these models offer insights into moderating online polarization by informing platform design and policy decisions regarding user interaction structures. Future research could explore extensions on dynamic networks with varying degree distributions or integrate external information sources to further analyze influence dynamics. These developments could deepen our understanding of social media’s impact on public opinion and contribute to strategies mitigating extreme polarization.

The implications of this research resonate with ongoing discussions in computational social science and network theory, laying groundwork for enriched models reflecting complex real-world social interactions. The paper complements the existing discourse on echo chambers and paves the way for actionable strategies informed by robust theoretical insights.