Numerical experiments for the analysis of manipulability in the extrapolation procedure based on the maximum likelihood method

The extrapolation procedure based on the maximum likelihood method (MLM) is one of the perspective collective choice procedures. In the analysis of collective choice procedures check of manipulability and determination of the degree of manipulability is essential. The above procedure is subject to manipulation by participants of choice. Carrying out evaluation of the degree of manipulability of the extrapolation procedure based on the MLM by using the developed to the present time indexes is impossible because of inadmissibility of existing assumptions to the mechanism of the procedure. In the paper an index of resistance of preference relation in a pair of alternatives from the collective ordering is proposed as a criterion of the degree of manipulability of the extrapolation procedure based on the MLM. In the article it is given description and results of numerical experiments carried out to determine the possibility of manipulability of the extrapolation procedure based on the MLM by using three ways of change of expertsʹ opinions at various values of the index of resistance for pair of alternatives from the ordering the most vulnerable to possible manipulation by participants of choice. A purpose of manipulation was to swap the positions of the alternatives from this pair in the collective ordering. On the basis of the results of experiments it is determined а range for threshold value of the index of resistance for pairs of alternatives from the ordering above which it is not observed manipulability of the extrapolation procedure based on the MLM in the three considered possible ways of manipulation by participants of choice. In each individual case exact threshold value of the index of resistance for pair of alternatives depends on number of permissible orderings corresponding to the changed opinions of the participants of collective choice.