A mathematical framework for probabilistic choice based on information theory and psychophysics

Risky decision-making (e.g. reward dependency) has been associated with substance abuse, psychopathy and pathological gambling; conversely, marked sensitivity to risk and uncertainty have been observed in anxiety disorder patients. In economic decision theory, probability and uncertainty have been dissociated. Frank Knight defined uncertainty as loss of information on the probability distribution of outcomes for choices (i.e., unpredictability), which is referred to as Knightian uncertainty (also as ambiguity). However, even when the probability distribution of outcomes is known, there are different degrees of predictability. In information theory, this type of degrees of uncertainty/unpredictability has been parametrized by introducing Shannon entropy. In the present paper, we show: (i) a mathematical framework combining Shannon entropy in information theory and Weber's law in psychophysics is capable of parametrizing subject's level of both aversion to probabilistic uncertainty (exaggerated in anxiety disorder patients) and reward dependency (enhanced in drug addicts and pathological gamblers), and (ii) this framework has an analogue in thermodynamics, therefore this can readily be utilized in studies in the nascent fields of neuroeconomics and econophysics as well. Future study directions for elucidating maladaptive personality characteristics in neuropsychiatric patients by using the present framework are discussed.