Development of an expert evaluation method using the gradient descent algorithm

The paper proposes a new expert evaluation method based on the use of gradient descent and matrix factorization, aimed at solving the problems of Delphi, analytic hierarchy process, Borda voting and clustering methods, such as limited objectivity, vulnerability to opinion polarization, limited scalability and vulnerability to collusion. The method uses latent factors to model the hidden preferences of experts and the characteristics of the evaluated options, which makes it possible to identify the most universally accepted decisions and neutralize the influence of biased groups. To test the model, a simplified version of it was implemented in Python, which allows simulating expert assessments taking into account polarization and random initial conditions. Experiments have shown that the method distinguishes high-quality, polarizing, neutral and low-quality variants based on the utility values of the variant, and also demonstrates resistance to initial conditions due to regularization. Compared with traditional methods, the developed approach provides higher accuracy, scalability and resistance to bias, although it requires large computing resources. The results confirm the practical significance of the method for data analysis tasks in conditions of large amounts of information and diverse expert opinions, making it a universal tool for decision support.