Order effects in sequential measurements of non-commuting psychological observables

Sequential measurements of non-commuting observables produce order effects that are well-known in quantum physics. But their conceptual basis, a significant measurement interaction, is relevant for far more general situations. We argue that non-commutativity is ubiquitous in psychology where almost every interaction with a mental system changes that system in an uncontrollable fashion. Psychological order effects for sequential measurements are therefore to be expected as a rule. In this paper we focus on the theoretical basis of such effects. We classify several families of order effects theoretically, relate them to psychological observations, and predict effects yet to be discovered empirically. We assess the complexity, related to the predictive power, of particular (Hilbert space) models of order effects and discuss possible limitations of such models.