Detection of Decision-Making Manipulation in the Pairwise Comparison Method

Abstract

Most decision-making models, including the pairwise comparison method, assume the honesty of the decision-maker. However, it is easy to imagine a situation where the decision-maker tries to manipulate the ranking results. This problem applies to many decision-making methods, including the pairwise comparison method. This article proposes three simple algorithmic methods for manipulating data using the pairwise comparison method. The proposed solutions try to mimic the behavior of a dishonest decision-maker who, acting under time pressure, chooses a simple strategy that leads to pushing through a given alternative. We also test the susceptibility to detection of the proposed manipulation strategies. To this end, we propose a convolutional neural network architecture, which we train based on generated data consisting of the original random pairwise comparison matrices and their manipulated counterparts. Our approach treats the pairwise comparison matrices as two- or three-dimensional images specific to the decision situation. In the latter case, the matrices are initially transformed into a three-dimensional map of local inconsistencies, and only data processed in this way are subjected to analysis using neural networks. The experiments indicate a significant level of detection of the proposed manipulations. In numerical tests, the effectiveness of the presented solution ranges from 88% to 100% effectiveness, depending on the tested algorithm and test parameters. The measured average computation time for the single case analyzed oscillated below one millisecond, which is a more than satisfactory result of the performance of the built implementation. We can successfully use the neural networks trained on synthetic data to detect manipulation attempts carried out by real experts. Preliminary tests with respondents also indicated high effectiveness in detecting manipulation. At the same time, they signaled the difficulty of distinguishing actual manipulation from a situation in which an expert strongly prefers one or more selected alternatives.

Keywords

• pairwise comparisons
• manipulation
• neural network
• machine learning
• AHP