Optimization of binary questionnaires

Optimal questionnaires may be obtained by using the principle of a root question. A binary relation introduced on the set of questions divides the questionnaires into transitive and nontransitive. For both classes theorems are formulated which limit the choice of the root question. For a univalent choice of the question relations are obtained which lead to an algorithm for design of an optimal questionnaire when additional conditions are met and an algorithm for design of a quasi-optimal questionanaire when they are not.