# Detection of Decision-Making Manipulation in the Pairwise Comparison Method
## 6 Experiments and Results  
This section explores the potential of using CNNs to detect manipulations in _PC_ matrices, describes the tuning process of the network structure, and presents the results of the experiments. To test the neural network's accuracy in detecting the use of the described algorithms, we first conducted a training process and then a series of experiments. A separate network was prepared to detect the use of each of the three attack algorithms. We repeated the neural network training process on PC matrix C of different sizes \(n\). To ensure that the results of the described algorithms are comparable, we have chosen the following standard input parameters:  
* \(\alpha\)--for the _naive_ algorithm, it is equal to the size of the _PC_ matrix \(C\); otherwise, it is a uniformly distributed random number between \(1.1\) and \(5\);
* \(r\)--index of the reference alternative, is always equal to the index of the highest ranked alternative evaluated from the initial matrix \(C\);
* \(p\)--index of the alternative to be promoted, randomly selected and different from \(r\). All matrices used in the experiments were generated as follows:
* first, a ranking vector \(w\) (\(3\)) of length \(n\) was generated;
* next, the ranking vector \(w\) was transformed into a consistent _PC_ matrix \(C\) using (7);
* finally, the matrix \(C\) was disturbed to ensure that its inconsistency (9) was greater than \(0\). To introduce disturbances, each value of the \(c_{ij}\) element, where \(j>i\), was multiplied by a uniformly distributed random number chosen from the experimentally chosen interval \([0.5,2]\). Subsequently, each \(c_{ji}\) was modified using (2). We generated and attacked \(10,000\)_PC_ matrices for each \(n\in\{3,4,\ldots,9\}\) and for each tested manipulation algorithm. A total of \(420,000\) samples of different sizes were generated and manipulated. Next, matrices were divided into two sets: one set, containing \(20\%\) of the samples, was used to evaluate the model, and the other set, containing \(80\%\) of the samples, was used to train the model. The attack detection rate \([\%]\) (the percentage of the samples in which the learned network was able to identify whether the matrix had been manipulated or not correctly) is shown in Table 1.  
Figure 4: A way to transform data for neural network processing. In this case, a two-dimensional (2-D) _PC_ matrix is flattened to a one-dimensional (1-D) vector. In the context of binary classification (manipulation detection), a fundamental understanding of the concepts of _false positives_ (FPs) and _false negatives_ (FNs) is essential for the evaluation and enhancement of predictive model performance. These concepts underpin the metrics employed in model evaluation and serve as the basis for sophisticated analytical techniques such as ROC (Receiver Operating Characteristic) analysis [80]. The numbers of _false positives_ and _false negatives_ were determined for a series of different matrix sizes, with a total of 4000 test matrices utilized per size for this purpose (Table 2). Moreover, we investigated the impact of introducing an upper threshold for the pairwise comparison values in the _basic_ algorithm. The attack detection rate (for \(7\times 7\) matrices) in such a scenario is shown in Table 3:  
Using the distance indicators ((14)-(16)) between the original and manipulated matrix allow us to tracking the size of the resulting manipulation. In the case of the \"advanced\" algorithm, this allowed us to detect a weak positive Pearson's correlation between the values of distance indicators (14) and (15), and the inconsistency value determined by [PERSON]'s _CI_ (Figure 5). This means that some cases of manipulation attack using this method can be detected by observing the inconsistency level of the PC matrix.