Averaging rules and adjustment processes in Bayesian inference

Abstract

Two empirically well-supported research findings in the judgment literature are (1)that human judgments often appear to follow an averaging rule, and (2) that judgments in Bayesian inference tasks are usually conservative relative to optimal judgments. This paper argues that both averaging and conservatism in the Bayesian task occur because subjects produce their judgments by using an adjustment strategy that is qualitatively equivalent to averaging. Two experiments are presented that show qualitative errors in the direction of revisions in the Bayesian task that are well accounted for by the simple adjustment strategy. Also noted is the tendency for subjects in one experiment to evaluate sample evidence according to representativeness rather than according to relative likelihood. The final discussion describes task variables that predispose subjects toward averaging processes.The Bayesian inference task is usually instantiated in terms of the " bookbag and poker chips paradigm" in which there are two competing hypotheses involving populations of binary events. For example, there may be two bookbags, one containing 70 red poker chips and 30 blue poker chips (the " red bag") and another containing 30 red chips and 70 blue chips (the " blue bag"). In most experiments, the experimenter ostensibly selects a bag at random and then draws samples from it one or more times. These samples are shown to the subject, usually sequentially, and the subject rates the strength of his or her belief about which bookbag was sampled.

Is the mind Bayesian? The case for agnosticism

“…In psychological literature, there appears to be an implicit convention according to which the term "Bayesianism" is almost always equated with the simple use of Bayes' identity (Ajzen and Fishbein 1975, Bar-Hillel 1980, Beyth-Marom and Arkes 1983, Birbaum 1983, Chase et al 1998, Fischhoff and Lichtenstein 1978, Gigerenzer and Hoffrage 1995, Girotto 1994, Griffin and Tversky 1992, Kahneman and Tversky 1972b, Lewis and Keren 1999, Lopes 1985, Manktelow 1999, McCauley and Stitt 1978, Mellers and McGraw 1999, McKenzie 1994a, Slovic and Lichtenstein 1971, Sedlmeier and Gigerenzer 7 2001, Stanovich and West 1999, Wolfe 1995. In these articles, the terms "Bayesian" or "Bayesianism" just refer to the use of Bayes' identity.…”

“…This has incited a number of investigators to give up Bayes' rule. One minimal step away consists of building alternative algebraic rules and comparing them with Bayes' identity (Anderson and Sunder 1995, Duh and Sunder 1986, Gigerenzer and Hoffrage 1995, Leon and Anderson 1974, Lopes 1985, McKenzie 1994a, Shanteau 1970, Troutman and Shanteau 1977. Going one step further, a few investigators have designed new descriptive models such as the gap model (Smith et al 1993) and Tversky's support theory (Tversky and Koehler 1994).…”

Ambiguity and uncertainty in probabilistic inference.

“…However, whereas the term, "anchoring-andadjustment* is quite general and could encompass a wide range of models (cf. Lopes, 1981; Einhorn a Hogarth, 1984), we have been quite specific as to the nature of this process in our tasks. Of greatest interest in this regard is The support for the hypothesized anchoring-and-adjustment strategy comaes from several sources.…”

(Non)Complementary updating of belief in two hypotheses

“…Though belief updating has been studied extensively (e.g., Anderson, 1981;Carlson & Dulany, 1988;Edwards, 1968;Hogarth & Einhorn, 1992;Lopes, 1985Lopes, , 1987Shanteau, 1970Shanteau, , 1972Shanteau, , 1975Wallsten & Manley Sapp, 1977), few have examined complementarity. One exception is Robinson & Hastie, 1985;Van Wallendael, 1989), who used suspects in a murder mystery as MEE hypotheses.…”