Where do probability judgments come from? Evidence for similarity–graded probability

Where Do Probability Judgments Come From? Evidence for Similarity–Graded Probability Peter Juslin (peter.juslin@psy.umu.se) Department of Psychology, Umea University SE-901 87, Umea, Sweden Hakan Nilsson (hakan.nilsson@97.polmag.umu.se) Department of Psychology, Umea University SE-901 87, Umea, Sweden Henrik Olsson (henrik.olsson@psy.umu.se) Department of Psychology, Umea University SE-901 87, Umea, Sweden Abstract This paper compares four models of the processes and representations in probability judgment. The models rep- resent three principles that have been proposed in the lit- erature: 1) the representativeness heuristic (interpreted as relative likelihood or prototype-similarity), 2) cue- based relative frequency, and 3) similarity-graded prob- ability. An experiment examined if these models account for the probability judgments in a category learning task. The results indicated superior overall fit for similarity- graded probability throughout training. In the final block, all models except similarity-graded probability were re- futed by data. Introduction Where do probability judgments come from? This ques- tion has been fiercely debated the last decades in re- search on judgment under uncertainty. In the late sixties the conclusion was that probability judgments are fairly accurate reflections of extensional properties of the environment such as frequencies (Peterson & Beach, 1967). This changed with the influential heuristics and biases program in the seventies and eighties, which emphasized that probability judgments are guided by intensional aspects like similarity (Kahneman, Slovic, & Tversky, 1982). The nineties saw a renewed interest in the idea that extensional properties are reflected in peoples’ probability judgments as specified by the eco- logical models (Gigerenzer, Hoffrage, & Kleinbolting, 1991; Juslin, 1994). A third alternative combines inten- sional and extensional properties in an exemplar model to produce similarity-graded probabilities (Juslin & Persson, 2000). Only rarely have these accounts been contrasted in studies that chart the processes and representations that underlie probability judgments. We compare four mod- els of how people make probability judgments in a category learning task. The task involves assessment of the probability that a probe with feature pattern t be- longs to one of two mutually exclusive categories, A or B. For example, a physician may assess the probability that a patient with symptom pattern t suffers from one of two diseases. The models represent three principles that have been proposed in the judgment literature: the representativeness heuristic (two versions), cue-based relative frequency, and similarity-graded probability. We present a category structure that allows us to con- trast predictions derived from these hypotheses. Representativeness Heuristic According to the representativeness heuristic, people judge the probability that an object or event belongs to a category on the basis of the degree to which it is rep- resentative of the category, or reflects salient features of the process that generated it (Kahneman et al., 1982). The representativeness heuristic is routinely evoked post hoc to explain cognitive biases but has not been subjected to careful tests in inductive learning tasks. A relative-likelihood interpretation of representative- ness states that the probability judgment p(A) that probe t belongs to A is made by comparing the likelihood of t in category A relative to its likelihood in categories A and B: p ( A ) = . 5 d + f ( t A ) d + f ( t A ) + f ( t B ) Eq. 1 where f(t|A) and f(t|B) are the relative frequencies of feature patterns identical to t in categories A and B, respectively. To allow for pre-asymptotic learning (Nosofsky, Kruschke, & McKinley, 1992) and response error in the use of the overt probability scale (Erev, Wallsten, & Budescu, 1994), all models in this paper are equipped with a free parameter d for dampening. The dampening effectively pulls the predictions to- wards . 5 (e.g., an un-dampened prediction of 1 becomes somewhat less extreme as a result of d). Eq. 1 implies that the probability judgment that, say, a patient with symptom pattern t has disease A is a direct function of