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Quantum approach to human cognition and behavior suffers from a so-called phase problem—lack of means to determine the phase parameter of quantum models before the experiment, which deprives them of predictive power and most of their potential practical impact. We report an empirically supported hypothesis which can help to resolve the issue. According to the hypothesis, the quantum phase between unresolved cognitive alternatives in a family of similar decision making situations is nearly constant across national, linguistic, and cultural backgrounds of subjects. If confirmed, the quantum phase stability phenomenon supplements the quantum model of decision making endowing it with predictive power. This possibility is demonstrated in the testing experiment where irrational behavior within previously unexplored social group could be probabilistically predicted with high accuracy. [ABSTRACT FROM AUTHOR]