The paper considered 3 models of decision-making about voting for or against a politician in a digital society. These models correspond to different levels of voter awareness with random interference. In 1st model the decision making problem is solved for an experienced voter who knows the Bayesian characteristics of interference. In 2nd model a less experienced voter makes decisions using the recommendations of experts. To determine the optimal parameter of the decision rule, a stochastic approximation is proposed. In 3rd model asymmetric awareness of voter and politician about socio-political potential is considered. In this case, an unscrupulous politician may understate the socio-political indicator in order to maximize own goal function. That shifts an estimation of decision rule parameter. The voter is considered as apprentice using the recommendations of the mentor (i.e. expert not aware of that potential) for estimation and voting under uncertainty caused by both random interference and politician unwanted activity. Apprentice's estimation and voting procedures constitute the voting mechanism. The set of politician choices has been determined, at which the maximum of his goal function is achieved with this voting mechanism. Sufficient conditions are proved for the synthesis of the optimal voting mechanism, in which politician chooses the socio-political indicator equal to the potential. So the optimal parameter of the decision rule is determined. Obtained results are illustrated by the example of a union of regional states governed by politicians elected by local societies.