The connection between the decision-making process and the opinion of community participating in the voting, which is given in the form of analytical expressions that are close to description of the voting process, as well as public opinion assessment are described in this paper. Analytical expressions that can be used in order to describe the voting process have been obtained. An approximate equation based on mathematical principles, in which a more detailed study of reality can be developed from a mathematical point of view is developed. Moreover, the significant influence of minor initial conditions on the voting process has been shown. The reliability of the results has been verified by computer simulation. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS'18).