The work is devoted to mathematical modelling of reflective processes - intensively developing branch of mathematical psychology.
A systematical statement of subject models is given in the work where the subject faces a moral choice, i.e. a choice of one of two polar alternatives:
first personifies good, and the second - evil.
A new, linear-square-law model of subject is offered, which allows combining nonlinear account of the subject's self-reflection and his opinion on actions of his partner, described in the linear way. A linear description of the partner appears to be natural because on the one hand it apreciably simplifies the model, on the other hand a person can estimate his own actions more subtly and in a more complicated manner than his partner's.
Two psychological problems are considered within the framework of the advanced approach, which demonstrate the offered model's effectiveness: analysis of the episode from Dostoyevskiy's novel 'Karamazoff brothers' and the research of the problem of totalitarian sects destructive influence.
Important influence of the subject optimism index on the accomplished choice is demonstrated on this material and one of the most important Christian principles 'Don't worry' is illustrated. It is also shown, that the orientation toward high or low optimism index value can serve as one of the criterions of difference between traditional confessions and totalitarian sects.