A joint analysis of the experimental data on cross sections of total and partial photoneutron reactions is performed for the 115In isotope. The data are obtained by using the quasimonoenergetic photons generated upon the annihilation of relativistic positrons. Well-known systematic discrepancies between the results of various experiments are analyzed using objective absolute criteria of data reliability and authenticity. Methods for taking these discrepancies into account are considered. New reliable and authentic evaluations for cross sections of the σ(γ, n), σ(γ2n), and σ(γ, 3n) reactions are obtained using the data on the cross section of the reaction of photoneutron total yields σ(γ,xn) in the context of a new experimental-theoretical approach to evaluating the cross sections of partial reactions. These data are free from the shortcomings of experimental methods for the photoneuron multiplicity sorting.