# Detection of Decision-Making Manipulation in the Pairwise Comparison Method
## 7 Discussion  
The experiments show that convolutional neural networks can accurately identify the manipulation methods described in Section 6 with high accuracy. These methods aim to provide a straightforward approach that aligns with the manipulative actions of an expert operating under time constraints and following the decision-making process [85]. We may observe this dishonest behavior in contexts such as sports or other clearly defined decision-making scenarios [86], where variables can be manipulated directly. The solution we present  
Figure 6: Design of neural networks used in the experiments.  
can be used in principle in any decision-making process using the pairwise comparison method. The prerequisite is access to suitable computing software. Detecting potential manipulation in practice can mean manually checking the data and having an expert decide on them or automatically excluding the indicated data as suspicious. Adopting one strategy or another depends on the person overseeing the decision-making process.  
While conducting the experiments, we discovered that simple indicators such as the error matrix (13) or inconsistency indexes (9) and (10) are insufficient for adequately training the neural network. We think some features of the manipulation algorithms are only detectable if more than two ranking values are compared simultaneously. Based on this observation, we introduced the determinant factor (17). We have also investigated other methods for transforming \(\mathbb{R}^{2}\)\(PC\) matrices to \(\mathbb{R}^{3}\) factors. However, we are still researching their impact on detecting attacks by neural networks.  
In the experimental setup, we used 2-D and 3-D convolutional layers with the same number of hidden neurons and layers for both cases. We achieved the optimal results for the 3-D models, although models with only one hidden layer can also produce acceptable results. The detection rates for the 2-D network, which has a similar design as shown in Figure 6, with the error matrix as a preprocessing step (Table 4).  
We used the (17) factor in the preprocessing step because the detection rate of the basic algorithm falls below our threshold. It is exciting that in contrast to the other algorithms, the _naive_ algorithm (Table 1) exhibits an increasing attack detection rate as \(n\) increases. Our interpretation is that in smaller matrices, pairwise comparison values are more often similar to each other. Nevertheless, our primary focus was on the attack detection rate. In addition, we calculated the number of _false positives_ and _false negatives_ (Table 2). Based on these values, we believe there is an opportunity to improve the architecture of our networks.  
The manipulation detection time for each algorithm increases depending on the matrix's size under consideration. In the small range of problem sizes studied, the increase is more or less linear despite the amount of data growing quadratically or cubically. This may be due to the relatively small size of the input data, which does not saturate the computational capabilities of the hardware. Computation time measurements are included in Table 5. The inconsistency of the matrices considered did not affect the results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(n\) & **Naive Algorithm** & **Basic Algorithm** & **Advanced Algorithm** \\ \hline
5 & 89 & 86 & 79 \\ \hline
6 & 95 & 77 & 80 \\ \hline
7 & 98 & 68 & 82 \\ \hline
8 & 99 & 67 & 83 \\ \hline
9 & \(\sim\)100 & 58 & 82 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Attack detection rate (using 2-D approach).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(n\) & **Naive Algorithm** & **Basic Algorithm** & **Advanced Algorithm** \\ \hline
5 & 491 & 504 & 488 \\ \hline
6 & 704 & 546 & 592 \\ \hline
7 & 686 & 660 & 651 \\ \hline
8 & 759 & 793 & 767 \\ \hline
9 & 945 & 964 & 945 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Manipulation detection time in \(\mu s\) for three algorithms: “naive”, “basic”, and “advanced”.