# Polarization in Political Rallies: A Markovian Agent-Based Model for Opinion Dynamics
## 6 Conclusions and Future Works  
In this paper, we propose the use of Markovian agents for agent-based opinion dynamics modeling. Markovian agents are particularly suitable for modeling asymmetric scenarios with different kinds of individuals, each with their own opinion, and complex scenarios.  
The proposed Markovian agent modeling framework complements existing approaches by providing a versatile and analytically tractable tool for studying opinion dynamics in temporally and spatially structured settings.  
We showed how the interactive Markovian agent modeling paradigm is able to capture interactions between individuals, also taking into account spatial distribution that affects their behavior.  
Our model demonstrated the ability to simulate the dynamics of opinion formation and polarization in a crowd during an electoral rally, where a speaker attempts to influence listeners with diverse initial opinions. The results highlighted the importance of the speaker's influence rate and the spatial distribution of listeners in determining the final consensus. Specifically, we observed that a higher speaker influence rate significantly increases the likelihood of achieving a majority consensus, particularly in scenarios where listeners are randomly distributed. Conversely, when listeners are clustered in a specific area, the speaker's influence becomes less effective, and achieving consensus requires more time and a higher influence rate.  
Figure 10: Transitory expiration time length \(T_{T}\) of _Random_ (**a**) and _Rectangular_ (**b**) configurations.  
One of the key advantages of our model is its ability to derive transient measures, which are crucial for applications where the focus is on understanding the evolution of opinions over a specific time frame rather than reaching a steady state. This is particularly relevant in the context of political rallies, where the goal is to maximize the number of convinced listeners within a limited time period. Our analysis of the transient phase revealed that the spatial distribution of listeners plays a significant role in the speed and extent of opinion change, with random distributions leading to faster and more widespread consensus compared to clustered distributions.  
Furthermore, the flexibility of our model allows incorporation of additional factors that could influence opinion dynamics, such as the presence of mass media or the introduction of multiple speakers with varying levels of influence. Future work could explore these extensions to provide a more comprehensive understanding of opinion formation in complex social networks.  
Another area of interest is the extension of the model to include more complex network structures, such as scale-free or small-world networks, which better reflect real-world social interactions. This could help in understanding how the topology of social networks influences the spread of opinions and the formation of consensus.  
Finally, empirical validation of the model using real-world data from political rallies, social media platforms, or other opinion-influencing events could enhance the model's applicability and provide more accurate predictions of opinion dynamics in various contexts. We plan to experiment with the Markovian agent approach using real-world data in future work.  
Conceptualization, M.S. and S.S.; methodology, M.S., F.L. and S.S.; software, M.S.; validation, M.S. and S.S.; formal analysis, M.S., M.G., F.L. and S.S.; investigation, M.S., M.G., F.L. and S.S.; resources, M.S.; writing--original draft preparation, M.S., M.G., F.L. and S.S.; writing--review and editing, M.S., M.G., F.L. and S.S.; supervision, M.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.