All-Moscow seminar "Expert opinion and data analysis"
On July 7, 2021 at 14:30, a joint meeting of the All-Moscow Seminar "Expert opinion and data analysis" and the seminar of the International Center for Decision Analysis and Choice of the Higher School of Economics took place.
Speaker: A.N. Subochev (HSE University)
The literature offers many different solutions to the problem of choosing the optimum based on the results of pairwise comparisons of options (tournament solutions). The properties of these solutions are generally well researched. Of particular importance is such a property as the stability of choice, understood as the independence of the selection results from the presence or absence of non-optimal alternatives in the set available for selection. Not all known tournament solutions possess this property, and this circumstance gives special value to those of them who have it. Due to the presence of stability, as well as other desirable properties, one of the candidates for the role of the best tournament solution is the so-called two-party set - the carrier of the maximum lottery on the tournament alternatives. This report is devoted to the consideration of the so-called essential set, proposed as a generalization of the two-party set to the practically important case of a weak tournament (tournament withdraws). The main tasks of the study, the results of which are presented in the report, were, firstly, to check the preservation by an essential set of a number of important properties of the two-party set, the presence of which justifies its use as an optimal choice tool, and secondly, to establish set-theoretic relations with generalizations of other important tournament solutions, and thirdly, checking on real data the quality of rankings obtained using a significant set.