  A mathematical model of Subject behaviour choice is proposed. The background
of the model is the concept of two preference relations determining Subject
behaviour. These are an "internal" or subjective preference relation and an
"external" or objective preference relation.
  The first (internal) preference relation is defined by some partial order on
a set of states of the Subject. The second (external) preference relation on
the state set is defined by a mapping from the state set to another partially
ordered set. The mapping will be called evaluation mapping (function).
  We research the process of external preference maximization in a fashion that
uses the external preference as little as possible. On the contrary, Subject
may use the internal preference without any restriction.
  The complexity of a maximization procedure depends on the disagreement
between these preferences. To solve the problem we apply some kind of the
successive approximations methods. In terms of evaluation mappings this method
operates on a decomposition of the mapping into a superposition of several
standard operations and "easy" mappings (see the details below). Obtained in
such way superpositions are called approximating forms.
  We construct several such forms and present two applications. One of them is
concerned with a hypothetic origin of logic. The other application provides a
new interpretation of the well known model of human choice by Lefebvre. The
interpretation seems to suggest a justification different from the one proposed
by Lefebvre himself.
