The Rational Basis of Representativeness
Representativeness is a central explanatory construct in cognitive science but suffers from the lack of a principled theoretical account. Here we present a formal definition of one sense of representativeness – what it means to be a good example of a process or category in the context of Bayesian inference. This analysis clarifies the relation between representativeness as an intuitive statistical heuristic and normative principles of inductive inference. It also leads to strong quantitative predictions about people’s judgments, which compare favorably to alternative accounts based on likelihood or similarity when evaluated on data from two experiments. Why do people think that Linda, the politically active, single, outspoken, and very bright 31-year-old, is more likely to be a feminist bankteller than to be a bankteller, even though this is logically impossible? Why do we think that the sequence HHTHT is more likely than the sequence HHHHH to be produced by flipping a fair coin, even though both are equally likely? The standard answer in cognitive psychology (Kahneman & Tversky, 1972) is that our brains are designed to judge “representativeness”, not probability: Linda is more representative of feminist banktellers than of banktellers, and HHTHT is more representative of flipping a fair coin than is HHHHH, despite anything that probability theory tells us. Not only errors in probabilistic reasoning, but numerous other phenomena of categorization, comparison, and inductive inference have been attributed to the influence of representativeness (or, under different names, prototypicality or “goodness of example”; Mervis & Rosch, 1981; Osherson, Smith, Wilkie, Lopez, & Shafir, 1990; Rips, 1975). However, a principled account of representativeness has not been easy to come by. Its leading proponents (Kahneman & Tversky, 1996; Mervis & Rosch, 1981) have asserted that representativeness should be defined only operationally, in terms of people’s direct judgments; an a priori, analytic definition need not be given. Consequently, critics have argued that the concept is either trivial or too vague to serve as an explanation of intuitive probability judgment (Gigerenzer, 1996). This paper presents a framework for constructing rational models of representativeness, based on a Bayesian analysis of what makes an observation a good example of a category or process. The goal of our analysis is to identify one precise sense of representativeness, and to show that it has a rational basis in normative principles of inductive reasoning. We will first point out some shortcomings of previous accounts of representativeness based on likelihood or similarity, and show how a Bayesian approach can overcome those problems. We will then compare the quantitative predictions of Bayesian, likelihood, and similarity models on two sizable datasets of representativeness judgments.