The article discusses the problem of political stability of a social system dependent on vital services (such as vaccination during the SARS-CoV-2 pandemic). Political stability is assumed to be achieved if society approves of the authorities' actions to increase the supply of these services. However, the possibilities of this supply depend on random factors unknown to society. This can be used by the authorities to achieve their goals, which do not necessarily coincide with the goals of society. Therefore, members of society must learn to recognize and evaluate the effectiveness of the actions of the authorities in the face of uncertainty. This problem is considered on the model of a socio-political system, which includes members of society - pupils, who are trained with the help of an adviser using machine learning procedures. Each pupil evaluates the performance of the politico responsible for providing vital social services. Political stability is guaranteed if each pupil regularly approves of his performance. Politico knows the potential of supply of those services better than the pupil and adviser. Therefore, politico can manipulate the real supply of services to get personal goals. Such unwanted activities of politico can result in decline in this supply. To avoid this, a scoring mechanism is proposed that includes an unsupervised machine learning of adviser, an adviser supervised machine learning of pupil, and the procedure of politico score. Sufficient conditions have been found for the synthesis of such scoring mechanism, at which politico uses all random possibilities of increasing the supply of social services are used. Such scoring mechanism is illustrated on the example of supply of vaccination services against coronavirus (COVID-19) in Northern Ireland.
