In modern political science (not only in Russia, but abroad as well) scholars are more constantly facing the question of the scientific picture of the world. It is particularly relevant under conditions of the tireless attempts to introduce natural-science methods into social sciences, to transform knowledge about socio-political processes into “positive knowledge.” The article covers a new and promising direction in the decision-making theory (a sub-discipline of political science), the so-called “quantum” approach. The authors turn to this approach in order to demonstrate the heuristic potential of the “quantum-like” theory of decision-making and to push forward the discussion about the scientific picture of the world in political science as a whole. The article deals with two types of decision-making models, which are the “quantum brain” model and the “quantum consciousness” model. Categories and basic conceptual solutions of those models were proposed, in particular, by A.Yu. Khrennikov, V.I. Yukalov, J.R. Busemeyer. Despite the great opportunities that these models provide researchers with, there are a number of limitations that are also characteristic of other decision-making theories. Moreover, the authors conclude that it is necessary to depart from binary logic in the given models and to start a more frank discussion over the issues of political and socio-psychological ontology. This applies in part to the use of open quantum systems as one of the categories in the “quantum-like” theory of decision-making. The authors note that the “quantum-like” theory of decision making has great theoretical and heuristic potential, and is probably an important element in the emerging scientific picture of the world in political science.