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.

Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities-this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed.

The Precautionary Principle has been an increasingly important principle in international treaties since the 1980s. Through varying formulations, it states that when an activity can lead to a catastrophe for human health or the environment, measures should be taken to prevent it even if the cause-and-effect relationship is not fully established scientifically. The Precautionary Principle has been critically discussed from many sides. This article concentrates on a theoretical argument by Peterson (2006) according to which the Precautionary Principle is incoherent with other desiderata of rational decision making, and thus cannot be used as a decision rule that selects an action among several ones. I claim here that Peterson's argument fails to establish the incoherence of the Precautionary Principle, by attacking three of its premises. I argue (i) that Peterson's treatment of uncertainties lacks generality, (ii) that his Archimedian condition is problematic for incommensurability reasons, and (iii) that his explication of the Precautionary Principle is not adequate. This leads me to conjecture that the Precautionary Principle can be envisaged as a coherent decision rule, again.