This paper deals with the problem of quantitative description and improvement of the quality of the service provided by taxi aggregator companies working on the Russian market. This problem seems to be insufficiently addressed in open research publications due to its high specificity, though some research aiming at searching the quality metrics have been conducted for some companies worldwide. The goal of the current research is mathematical formalization of a rating system assessing the driver service quality that allows one to design a parametrically tunable model. The proposed mathematical model of the rating system is described by means of a state graph where the transition from a vertex to another happens when the explicitly written conditions are satisfied. We show that the rating evaluation for a driver remaining in the active can be carried out by means of linear filtration performed as digital signal processing of the time series consisting of the scores which are given to the driver by their passengers. The type and waveform of the filter impulse response is suggested. The A/B-test conducted for the group of drivers working with a taxi aggregator proved the fact that the integral metric of service quality is sensitive to changes in the parameters of the proposed rating system; this eventually led to a decrease in the rate of taxi rides accompanied with a negative client experience. The rating system model developed can be utilized to increase the quality of the service provided by the taxi aggregator by means of more effective differentiation of the drivers, while the subsequent optimization of the rating system parameters can serve as a tool for achieving indicators supporting the strategic goals of the company.