The article examines the problem of managing a democratic socio-economic system in the face of a shortage of a vital commodity (such as the COVID-19 vaccine). The citizens' approval of the actions of the authorities to increase the production and supply of this product contributes to political stability. The possibilities of increasing the supply of a vital commodity depend on random factors. In the face of such uncertainty, in the age of artificial intelligence, the management of a socio-economic system can be based on machine learning and adaptation. In this case, it is necessary to take into account the activity of the elements of the system associated with the presence of their own goals, which do not necessarily coincide with the goal of the system as a whole. These elements can influence adaptation and machine learning procedures to achieve their goals. The research is carried out on a three-level model of a democratic socio-economic system. At its top level is a member of society - a citizen who evaluates the politician who is at the middle level of the system. In turn, the politician can influence the increase in the supply of a vital commodity, including both its purchase on the market and production at a local plant belonging to the lower level of the system. Political stability is guaranteed if the citizen regularly approves the actions of the politician to increase the supply of vital goods. But the plant's management knows its own production potential better than the politician. Thus, this leadership can manipulate the volume of its own production in order to gain more support from the politician. A politician may also manipulate the opportunities available to him in order to achieve personal goals. To avoid manipulation of the supply of a vital product under conditions of uncertainty, a socio-economic management mechanism is proposed, including an economic and political mechanism. The economic mechanism includes a procedure for adaptive forecasting of the production of a vital commodity, as well as a procedure for supporting this production. The political mechanism includes a procedure for machine self-learning of a citizen, as well as a procedure for assessing the activity of a politician. Sufficient conditions for the synthesis of the optimal mechanism of socio-economic management are found, in which random opportunities to increase the supply of a vital commodity are fully used, including both purchases on the market and production at a local plant. An example of such a socio-economic mechanism is considered on the example of the supply of the COVID-19 vaccine to England.