## 4 Results
### Topic Models
In contrast, the all-MiniLM-L6-v2 embedding showed increased computation times, particularly at higher topic counts, although it remained below 7 s. This suggests a trade-off between embedding performance and computational efficiency. Figure 3 further explores the computational time associated with different embeddings for the Join platform. Notably, all embeddings exhibited a consistent computation time that remained stable across various topic counts, with the all-mpnet-base-v2 and BAAI/bge-large-en-v1.5 embeddings exhibiting slightly higher times compared to the other models. Figure 6 presents a comparison of the performance of different sentence embedding models in topic modeling for the iVoting platform, evaluated using the Normalized Point-wise Mutual Information (NPMI) metric. The embeddings tested include all-MiniLM-L6-v2, all-mpnet-base-v2, BAAI/bge-base-en-v1.5, BAAI/bge-large-en-v1.5, and BAAI/bge-small-en-v1.5, with the number of topics varying from 10 to 50. Among the models, BAAI/bge-base-en-v1.5 consistently achieves the highest NPMI scores, indicating superior topic coherence, particularly as the number of topics increases beyond 20. In contrast, all-mpnet-base-v2 and BAAI/bge-large-en-v1.5 exhibit lower coherence across most topic numbers, with notable drops in performance when the number of topics exceeds 30. The all-MiniLM-L6-v2 model performs relatively stably but remains slightly behind BAAI/bge-base-en-v1.5 in overall coherence. While BAAI/bge-small-en-v1.5 shows more variability in its performance, it demonstrates a recovery in NPMI as the number of topics increases beyond 30. These results suggest that BAAI/bge-base-en-v1.5 is the most effective embedding model for thematic analysis on the iVoting platform, providing the highest coherence across various topic configurations. Similarly, Figure 8 compares the different embeddings on the Join platform. Figure 7 illustrates the computational time required by various embedding models during topic modeling on the iVoting platform, as a function of the number of topics. The models evaluated include all-MiniLM-L6-v2, all-mpnet-base-v2, BAAI/bge-base-en-v1.5, BAAI/bge-large-en-v1.5, and BAAI/bge-small-en-v1.5. Among these models, BAAI/bge-large-en-v1.5 consistently exhibits the longest computational times, with a noticeable peak when the number of topics is around 20, reaching approximately 7 s. In contrast, the BAAI/bge-small-en-v1.5 model demonstrates the lowest computational times, staying below 4 s across all topic configurations. The all-mpnet-base-v2 model starts with relatively high computation times around 5 s but stabilizes as the number of topics increases. The all-MiniLM-L6-v2 model shows a gradual decrease in computational time as  
Figure 7: Comparison of different embeddings on iVoting regarding their computational time and the number of topics per topic model. the number of topics increases, performing similarly to BAAI/bge-small-en-v1.5 at higher topic counts. BAAI/bge-base-en-v1.5 remains stable, with moderate computation times slightly above 4 s. Overall, these results indicate a clear trade-off between computational efficiency and model size, where smaller models like BAAI/bge-small-en-v1.5 offer significantly faster processing times while larger models such as BAAI/bge-large-en-v1.5 demand more computational resources. In summary, the computational time results on Join suggest that larger models like BAAI/bge-large-en-v1.5 incur significantly higher computational costs, while smaller models, particularly BAAI/bge-small-en-v1.5, offer much faster processing times, making them potentially more suitable for large-scale or time-sensitive e-participation tasks. Figure 9 displays the computational time required by different embedding models for topic modeling on the JOIN platform, plotted against the number of topics. The models under comparison include all-MiniLM-L6-v2, all-mpnet-base-v2, BAAI/bge-base-en-v1.5, BAAI/bge-large-en-v1.5, and BAAI/bge-small-en-v1.5.