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Control over Recommendation Algorithms in Heterogeneous Modular Systems with Dynamic Opinions
Vladislav Gezha1, Ivan Kozitsin1
1Laboratory of Active Systems, V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia.
Entropy (Basel, Switzerland)
|March 28, 2026
Summary
This study introduces a framework for optimal ranking algorithms to shape societal opinions through agent interactions. It develops a mathematical model to control these interactions and achieve desired opinion distributions, like reducing polarization.
Area of Science:
- Computational Social Science
- Network Science
- Mathematical Modeling
Background:
- Opinion formation dynamics are complex, influenced by agent interactions and attributes.
- Designing interventions to steer collective opinions requires robust theoretical frameworks.
- Existing models often lack mechanisms to dynamically control interaction probabilities based on agent characteristics.
Purpose of the Study:
- To develop a model-dependent theoretical framework for optimal ranking algorithms.
- To design algorithms that achieve specific macroscopic opinion configurations.
- To investigate the control of opinion dynamics in agent-based systems.
Main Methods:
- A mean-field approximation (MFA) was derived as a nonlinear ordinary differential equation.
- A control problem was formulated to dynamically adjust ranking algorithm parameters.
- Finite-difference schemes were used to solve the control problem for a two-element opinion space.
Main Results:
- The existence of a solution for the control problem was proven, with properties of optimal controllers derived.
- A solution was obtained for any number of agent types, independent of external factors like social bots.
- Numerical tests validated findings and explored high-dimensional opinion spaces, including depolarization and nudging scenarios.
Conclusions:
- The proposed framework enables the design of optimal ranking algorithms for controlling opinion dynamics.
- The mathematical model and control strategies are effective in steering societal opinion configurations.
- This research offers a novel approach to understanding and influencing collective behavior in complex social systems.
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