Testing quantum-like models of judgment for question order effect

Lately, so-called “quantum” models, based on parts of the mathematics of quantum mechanics, have been developed in decision theory and cognitive sciences to account for seemingly irrational or paradoxical human judgments. In this paper, we limit ourselves to such quantum-like models that address order effects. It has been argued that such models are able to account for existing and new empirical data, and meet some a priori predictions. From the quantum law of reciprocity, we derive new empirical predictions that we call the Grand Reciprocity equations, that must be satisfied by quantum-like models on the condition that they are non-degenerate. We show that existing nondegenerate quantum-like models for order effects fail this test on several existing data sets. We take it to suggest that degenerate quantum-like models should be the focus of forthcoming research in the area. “Research is needed which designs tests of quantum properties such as the law of reciprocity” (Busemeyer and Bruza 2012, 342)