The Analytic Hierarchy Process (AHP) is a methodology of multiple-criteria decision making widely applied in order to synthesise local preferences across a complex hierarchy structure into global priorities, when multiple persons are involved in the considered decision making problem. Within its frame, numerous techniques have been developed for the priority evaluation. These techniques include classic eigenvector synthesis and multiplicative geometric means, three-dimensional eigenvectors, and simultaneous linear and nonlinear estimations by whole hierarchy structure in the synthetic optimising procedures. The paper considers and compares these techniques. To measure the quality of fit for all paired comparison matrices by the obtained vectors, a characteristic similar to the coefficient of multiple determination in regression analysis is suggested. A numerical example from marketing research with many criteria, subcriteria, alternatives and respondents is also presented for demonstration purposes. The quality of the approximation of the different considered approaches showed through the numerical example that the best results are produced by the nonlinear synthetic priority techniques. The described techniques have been successfully used in numerous real-world problems and are very helpful in serving the practical aims of managerial decision makers. The paper is arranged in 4 sections. The first section provides an introduction to the subject matter of the paper. Section 2 describes the various AHP techniques for local and global priority estimations, while Section 3 presents numerical results. Finally, Section 4 summarises the findings of the paper.