Bayesian inference: Combining base rates with opinions of sources who vary in credibility.

Abstract

Michael H. BirnbaumUniversity of Illinois at Urbana-ChampaignBarbara A. MellersUniversity of California, BerkeleySubjects made judgments of the probability of an event given informationand the opinion of a source. Base rate and the source's hit and false-alarm rateswere manipulated in a within-subjects design. Hit rate and false-alarm rate weremanipulated to produce sources of varied expertise and bias. The base rate, thesource's opinion, and the source's expertise and bias all had large systematic effects.Although there was no evidence of a base-rate fallacy, neither Bayes' theoremnor a subjective Bayesian model that allows for conservatism due to misperceptionor response bias could account for the data. Responses were consistent with a scale-adjustment averaging model developed by Birnbaum & Stegner (1979). In thismodel, the source's report corresponds to a scale value that is adjusted accordingto the source's bias. This adjusted value is weighted as a function of the source'sexpertise and averaged with the subjective value of the base rate. These results areconsistent with a coherent body of experiments in which the same model couldaccount for a variety of tasks involving the combination of information fromdifferent sources.The question, How should humans revisetheir beliefs? has been studied by philosophersand mathematicians, and the question, Howdo humans form opinions and revise them?has been investigated by psychologists. Earlyresearch that compared the two questionsconcluded that Bayes' theorem was a usefulstarting point for the description of humaninference but that humans are conservative,or revise their probability judgments in amanner less extreme than implied by Bayes'theorem (Edwards, 1968; Peterson & Beach,1967; Slovic & Lichtenstein, 1971).Edwards (1968) discussed three interpre-tations of conservatism: misperception, mis-aggregation, and response bias. Misperceptionincludes the possibility that objective proba-bilities are transformed to subjective proba-bilities by a psychophysical function. Misag-gregation refers to use of a non-Bayesian ruleto combine evidence. Response bias refers tononlinearity in the judgment function relatingjudged probabilities to subjective likelihoods.Early experimental work attempted to separate