On heuristic methods of obtaining the median in group choice problems

Obtaining the median of a specified set of relations is a widely used and legitimate way to determine the decision of a team of experts. An algorithm is described of locally functional optimization in an arbitrary fixed range of relations whose particular cases the numerous well-known ranking, classification, and ordered classification algorithms. With very natural assumptions on probability distributions on a set of individual expert-made decisions the accurate and locally-optimal medians are proved consistent.