A quantum probability perspective on the nature of psychological uncertainty

A quantum probability perspective on the nature of psychological uncertainty Lee C. White (l.c.white.517813@swansea.ac.uk) Department of Psychology, University of Swansea, Singleton Park, Swansea, SA2 8PP UK. Emmanuel M. Pothos (e.m.pothos@gmail.com) Department of Psychology, City University London London, EC1V 0HB UK. Jerome R. Busemeyer (jbusemey@indiana.edu) Department of Psychological and Brain Sciences, Indiana University, Bloomington 47468 Indiana, USA. Abstract Making a choice between alternatives can influence our subsequent evaluation of the selected option (e.g. Sharot, Velasquez & Dolan, 2010). Thus, in resolving psychological uncertainty, the act of making a judgment itself appears to have a constructive role in subsequent related decisions. This study focuses on emotional ambivalence and the development of affective evaluations over two stages, such that (just) making an intermediate evaluation in the first stage is shown to influence the overall affective evaluation in the second stage. Models based on classical probability theory, which assume that an intermediate evaluation simply reads off an existing internal state, cannot accommodate this result in a natural way. An explanation is offered with a quantum probability model, which, under specific circumstances, requires the measurement of an internal state to have a constructive role. The predictions of the quantum probability model were supported by the empirical results. Keywords: Quantum Affective uncertainty. probability; Interference effects; Introduction One basic fact about cognition is that it reflects uncertainty. In fact cognition appears to involve several kinds of uncertainty. As well as uncertainty regarding future events, there is uncertainty about internal states, an inevitable consequence of the fact that life events are often agglomerations of pleasant and unpleasant components. For example, consider ‘emotional ambivalence’, the apparent ability of the cognitive system to concurrently represent positive and negative affect. Emotional ambivalence is reflected in e.g., students’ thoughts about graduation day or advertisements with mixed emotional appeals (Larsen, McGraw & Cacioppo, 2001; Williams & Aaker, 2002). Understanding how the cognitive system resolves affective uncertainty presents challenges (e.g. Brehm & Miron, 2006). For example, is positive and negative affect experienced sequentially or simultaneously? What happens when people are asked to make a judgment about their affective state whilst experiencing affective uncertainty? Does this judgment resolve uncertainty or does the act of making the judgment itself influence their affect in the same way that choice has been shown to have a constructive influence on preference (e.g. Sharot, Velasquez & Dolan, 2010)? Our objective in this paper is to propose an ambitious new perspective on this question, based on quantum probability (QP) theory (note that in this work by QP theory we simply mean the rules for how to assign probabilities to events from quantum theory; for more specific proposals see Aerts, 2009, or Atmanspacher, Romer & Wallach, 2006). We can acquire some preliminary intuition from models for response times in choice problems, such as random walk models (e.g., Ashby, 2000; Busemeyer & Townsend, 1993; Ratcliff & Smith, 2004; Usher & McClelland, 2001). In this influential class of models, discriminating between two options involves an accumulation of evidence, so that, on every step, the weight for a particular option is increased. Crucially, at any time point, the system is assumed to be in a specific state. This state may reflect large or little weight for a particular option, but, regardless, it has to be at a specific state. Classical approaches must assume that the system is always at a particular state, even if knowledge of this state is uncertain. Such an assumption seems straightforward. How else could we build a model? Yet, there is an alternative, intriguing possibility, which emerges from the recent uses of QP theory in cognitive modeling (Busemeyer & Bruza, 2012; Pothos & Busemeyer, in press). QP theory is a framework for assigning probabilities to observables and, therefore, potentially relevant wherever there is a need to formalize uncertainty. QP cognitive models often have the same intentions (Griffiths et al., 2010; Oaksford & Chater, 2007) as classical probability models. But, classical and QP frameworks are founded on different axioms. QP models incorporate certain unique features, such as superposition and the capacity for interference, and there has been growing interest in exploring the relevance of such features for cognitive modeling (e.g., Aerts, 2009; Atmanspacher, Filk & Romer, 2004; Blutner, 2009; Busemeyer, Pothos, Franco & Trueblood, 2011; Khrennikov, 2010; Pothos & Busemeyer, 2009; Wang et al, in press).