The article considers the problem of determining the construction of a linear order of alternatives based on multiple comparisons of alternatives given by experts. In the electoral systems of different countries of the world, this approach is called preferential voting. The problem has wide practical applications and is successfully used in various spheres of human life. It is proposed to use an algebraic approach to solve this problem. In this case, to formalize the problem, the metric of rank mismatch of alternatives, sometimes called the Cooke metric, is used. In determining the resulting ranking, it is proposed to use simplifying heuristics that reflect different approaches to understanding the optimality of the resulting ranking. The problem of determining the resulting ordering of alternatives based on incomplete rankings or multiple comparisons is solved. A short list of classical voting methods and a scheme for solving the problem is given. An algorithm for determining the leader in the team and ensuring conflict-free preliminary voting is proposed and substantiated.