## 3 Group Decision-Making with Consensus Based on Subjectivity and Sentiment Analysis
### Group Decision-Making with Consensus Measures  
Once the preferences have been calculated from the transcripts of the discussion text, the group decision-making process with consensus can begin. To do this, the method will follow the steps described below:  
1. Preferences calculation. In the previous section, we used sentiment analysis on the debate transcripts to calculate the preferences of each expert on each alternative. To do this, we created sets of texts for each alternative and expert and extracted the preferences using a sentiment analysis process. The great advantage of this process is that the experts do not have to explicitly provide the preferences to the system. In the following, we will use this information to initiate a decision-making process. We will represent the expert's preference \(e_{i}\) over the alternative \(x_{j}\) as \(p_{ij}\). \(p_{ij}\) is a value located \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Value** & & **Linguistic Label** \\ \hline
0.75 & 1.00 & 1.00 & Very high \\ \hline
0.50 & 0.75 & 1.00 & High \\ \hline
0.25 & 0.50 & 0.75 & Medium \\ \hline
0.00 & 0.25 & 0.50 & Low \\ \hline
0.00 & 0.00 & 0.25 & Very Low \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Linguistic variable definition. Figure 6: Sentiments and emotions for each post. Figure 7: Sentiments associated to the posts. in the interval [0, 1], with 0 indicating a total disagreement with the alternative and 1 a total agreement with it. 2. Consensus calculation. Once the alternatives have been defined, it is possible to calculate the consensus associated with the round of the decision-making process. To do this, we will measure the closeness of the experts' opinions to obtain a degree of consensus. As we know, in practice, it is sometimes not possible to reach a full and unanimous consensus, but it is important to try to get experts to debate and bring positions closer together. The goal of consensus measures is to help decision-makers reach an agreement on the best solution to a decision-making problem. Therefore their role is increasingly important in solving group decision-making problems. In this article, we propose two different measures of consensus. One measures the closeness of opinions and the other compares experts according to the subjectivity of their opinions. To calculate consensus based on opinion, we use the following expression: \[\widehat{CA}=\frac{\sum_{j}CA}{n}\] (6) where: \[CA_{j}=\frac{\sum_{i}p_{ij}}{m}\] (7) where \(n\) is the total number of alternatives and \(m\) is the number of experts. For the calculation of the consensus based on the subjectivity of their opinions, we can use the following expression: \[P_{+ei}=\frac{N_{ptw}}{N_{ttw}}\] (8) \[P_{-ei}=\frac{N_{ntw}}{N_{ttw}}\] (9)  
Expression (8) is for positive words and Expression (9) is for negative ones. The measure of subjectivity in the debate is a key detail that can help us determine which experts show a more vehement attitude in the discussion and which, on the contrary, are more passive or indifferent to the subject under debate. Once the consensus has been calculated, the following two actions can be carried out:  
* Invite those experts who have a view that is far from the rest to join the consensus. * Try to motivate experts who are more passive in the debate to be more participatory. Thanks to these two actions, we try to involve all experts as much as possible in the debate. It is very important that they try to discuss and bring positions closer together in order for the final decision to be as consensual as possible. It is also important that all experts are involved in reaching it. To motivate experts to try to reach consensus, it is possible to set a threshold above which, if not exceeded, experts are allowed to conduct a longer discussion. Our method allows thresholds to be set for both measures. However, for the sake of brevity, we will set only a consensus threshold of \(\gamma\) for the opinion-based consensus measure. 3. Calculation of the collective preference matrix and final ranking.