Human Judgment and Imprecise Probabilities

The study of human judgment under uncertainty has a history that is almost contemporaneous with that of probability theories. This is not a coincidence. From the outset, the idea of using probability to describe cognitive states or aspects of subjective judgment has provoked debate, theory construction, and empirical research. It is no exaggeration to say that probability theories have exerted a strong prescriptive influence on the study of judgment and decision making (see Gigerenzer 1994 [21] and Smithson 1989 [41] for overviews). In the modern era, proponents of the Subjective Expected Utility (SEU) framework advocated a version of Bayesianism as the benchmark for rational judgment and decision making, and this viewpoint dominated studies of human judgment and decision making during the 50’s and 60’s. By the late 70’s and early 80’s, some scholars had begun to question whether we should regard deviations from probability theories as “irrational” (cf. Cohen 1981 [9], Jungermann 1983 [29]), and attempts to develop descriptive theories of decision making that retained as many features of SEU as possible became a small-scale industry among decision scientists. However, most of these critiques and alternatives have left certain Bayesian prescriptions unquestioned. Two of these are directly relevant to the study of imprecise probabilities: • Precision, i.e. the doctrine that uncertainty (or utility as well) may be represented by a single number; and • Prior sample space knowledge, i.e. the assumption that all possible outcomes or alternatives are known beforehand. Accusations against Bayesians of over-precision and arbitrariness in their priors date back to the mid-19th century, but empirical studies of how people deal with imprecision were rare until the mid-1980’s and to this day there are almost no studies of how people cope with sample space ignorance. In terms of reasonable combinations from Table 1, the vast majority of empirical studies deal with situations where probabilities are precise, outcomes are known, and the utilities of all outcomes are precise (cell 1). A much smaller but growing literature concerns situations with vague probabilities but known outcomes (usually with precise utilities—cell 2). A still smaller set of studies deals with imprecise utilities and/or partly known outcomes. Very few studies venture any further into imprecision or ignorance than that (but see, for instance, Hogarth & Kunreuther 1995 [28]). Early attempts to develop descriptive as well as prescriptive frameworks for decision making when probabilities are unknown (but not necessarily when outcomes