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The  article  describes  in  detail  the  effect  named  “united  voting”.  This  effect  allows  making  the  right  choice  when  the  correct  solutions  comprise  a  very  small  part  of  the  solution  set.  This  choice  is  pos-sible if the erroneous solutions are randomly distributed evenly across the solution set. In the proposed method the obtained solutions are reflected in the histogram, and it is necessary to organize its accu-mulation and analysis in such a way that a remarkable extremum is formed in the position of the cor-rect solution. A formal description of the situations in which this effect can be utilized is given. For two real functions in Euclidean space, it is necessary to find such parameters of the affine transformation of one of the functions that will make it similar to the second function at least locally. A formal descrip-tion of both the problem and the proposed solution method allows for the application of this approach in a variety of situations. The main technological features that need to be taken into account in order to find the right solution and evaluate its reliability are considered. As an example of the implementationof the proposed approach, a program is described, which searches shift between images of the Earth’s surface taken at a different time. The results of its testing are presented. Possible ways of further genera-lization of this method of data analysis are noted.