Testing bayes rule and the representativeness heuristic: Some experimental evidence

Abstract

The psychological literature has identifi ed a number of heuristics which individuals may use in making judgements or choices under uncertainty. Mathematically equivalent problems may be treated differently depending upon details of the decision setting (Gigerenzer et al. (1988), Hinz et al. (1988), Birnbaum and Mellers (1983), Ginossar and Trope (1987)) or upon how the decisions are framed (Tversky and Kahneman (1986)). The results presented in this paper are consistent with those fi ndings and are unsettling. In equivalent problems subjects appear to adopt different strategies in response to observing different data. All problems were inference problems about populations represented by bingo cages and all randomization was operational and observed by the subjects. Thus one cannot explain the change of decision strategy by appeal to changing reference points nor should difference between surface and deep structure of problems apply (Wagenaar et al. (1988)). A striking observation from the experiments is the result of employing financial incentives. Some experiments included financial incentives for accuracy and some did not. In the latter experiments the number of nonsense or incoherent responses increased by a factor of three. The majority of subjects in both treatments behaved reasonably, but of those lacking fi nancial incentives a larger proportion gave obviously absurd responses. This suggests that data from decision experiments in which no financial incentives were should be treated as possibly contaminated and statistical methods robust against outliers employed.

On the reality of cognitive illusions.

“…He claims that "If one lets the subjects do the random drawing base-rate neglect disappears" (1991, p. 100). This claim is inconsistent with the data: Underweighting of base-rate was demonstrated in several studies in which participants actually drew random samples from a specified population, such as numbered balls from a bingo cage (Camerer, 1990: Grether, 1980, 1992Griffin & Dukeshire, 1993). Even in Gigerenzer's own study, all six informative descriptions deviated from the Bayesian solution in the direction predicted by representativeness; the deviations ranged from 6.6% to 15.5%(seeGigerenzeretal., 1988, Table 1, p. 516).…”

The trouble with overconfidence.

“…Although judgments do sometimes adhere to Bayesian principles remarkably well (Ajzen, 1977;Griffiths & Tenenbaum, 2006;Kersten, Mamassian, & Yuille, 2004), human judgment certainly does not obey Bayes's Law perfectly (Edwards, 1968;Grether, 1990;McKelvey & Page, 1990).…”

Estimating subjective probabilities

“…Karni [2009], Grether [1992, Köszegi and Rabin [2008], and Holt and Smith [2009] are examples of this alternative. Let there be two prizes, x>y.…”

“…In effect, the score or payment penalizes the subject by the squared deviation of the report from the true binary-valued outcome, 1, which is 1 3 There exist mechanisms that will elicit subjective probabilities without requiring that one correct for risk attitudes, such as the procedures proposed by Köszegi and Rabin [2008;p.199], Karni [2009], Grether [1992, Holt andSmith [2009], andOfferman, Sonnemans, van de Kuilen andWakker [2009], discussed further below. The latter three employ these mechanisms in an experimental evaluation.…”