Testing quantum-like models of judgment for question order effect

Abstract

a b s t r a c tLately, 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. We consider here some such quantum-like models that address question order effects, i.e. cases in which given answers depend on the order of presentation of the questions. Models of various dimensionalities could be used; can the simplest ones be empirically adequate? From the quantum law of reciprocity, we derive new empirical predictions that we call the Grand Reciprocity equations, that must be satisfied by several existing quantum-like models, in their non-degenerate versions. Using substantial existing data sets, we show that these non-degenerate versions fail the GR test in most cases, which means that, if quantum-like models of the kind considered here are to work, it can only be in their degenerate versions. However, we suggest that the route of degenerate models is not necessarily an easy one, and we argue for more research on the empirical adequacy of degenerate quantum-like models in general.

Quantum-like models cannot account for the conjunction fallacy

“…We have tested three empirical predictions of these models: the GR equations (Boyer-Kassem et al 2016) that apply to non-degenerate versions only of the models, the existence of an order effect and the QQ equality , which apply to both non-degenerate and degenerate versions of the models, hence to the most general version of the papers. Such tests cannot be performed in traditional conjunction fallacy experiments, in which subjects have to rank propositions, but require an order effect experiment, in which two yes-no questions are asked in either order.…”

“…Moreover, if quantum-like models were to apply to some cases of conjunction fallacies, it seems very likely that it should be degenerate versions, since non-degenerate ones have been strongly ruled out. This comes with possible drawbacks or specific duties, as argued in Boyer-Kassem et al (2016). In particular, a degenerate model resorts to some extra dimensions in the Hilbert space that should receive theoretical and experimental justifications so as not to be just ad hoc, and more general tests on elementary dimensions can also be considered.…”

“…This comes from the projection postulate that modifies the state of belief when an answer is given to a question. This order effect property of the quantum-like models is well known, and it has actually been used to provide a quantum-like account of order effect (see for example Conte et al 2009;Busemeyer et al 2009Busemeyer et al , 2011Atmanspacher and Römer 2012;Pothos and Busemeyer 2013;Wang and Busemeyer 2013;Wang et al 2014;Boyer-Kassem et al 2016)-thus, the same models are at the basis of the account of order effect and of the conjunction fallacy. Fig.…”

Une nouvelle approche expérimentale pour tester les modèles quantiques de l’erreur de conjonction

“…Pourêtre légitime, une explication doit reposer sur des modèles empiriquement adéquats. Aussi, nous poursuivrons ici l'étude de l'adéquation empirique de ces modèles quantiques, dans la lignée de travaux ré-cents (e. g. , Pothos et Busemeyer 2013, Busemeyer et al 2015, Boyer-Kassem et al 2016. L'originalité de notreétude consistè a avoir conçu et realisé un protocole experimental qui permet d'observer l'erreur de conjonction comme un effet résultant d'un autre biais cognitif (l'effet d'ordre).…”

“…Cependant, le choix entre les deux types de modèles n'a pasété définitivement arrêté. Nous proposons donc d'adapter un test proposé par Boyer-Kassem et al (2016), consistantà vérifier si deséquations dites « GR » sont vérifiées.…”