Performance in a multiple alternative Bayesian decision task: as a function of sample size and order of evidence

Abstract

This study was concerned with human decision making under conditions of uncertainty. Roby's Belief-State model, which is based on Bayes' theorem, was employed as the normative model in the present investigation. Based upon their knowledge of a bowman's ability as a marksman {conditional probabilities) and the accumulating evidence describing the point of impact of his arrows, Ss estimated the probabilities that the bowman was aiming at each of four quadrants on a target (posterior probabilities}. Subjects engaged in a sequential decision task. That is, the posterior probabilities estimated at trial t became the prior probabilities at trial t + 1. An increase in Sample Size, the number of clues Ss observed prior to their revision, did not result in a decrease in performance accuracy as measured by the subjective estimate as, signed to the correct alternative (Verified Certainty Score}. Evidence from an analysis of Performance Index scores (Edwards & Phillips, 1964) suggested that accuracy may be enhanced by an increase in Sample Size. While Ss in Sample Size conditions Four and Eight were not affected by changes in the order of clue presentations, Ss in Sample Size conditions One and Two were affected. The results indicated that these latter Ss were not commutative. Subjects in the present task exhibited a recency effect in revising their estimates. It appeared as if the combined effects of recency and conservatism accounted for Ss' performance more accurately than did a combination of conservatism and the Bayesian model. Bayes' theorem does not appear to be a useful model for revision of subjective probability estimates when Ss are operating in a nonstationary environment. In the present task, Verified Certainty Score, the subjective estimate assigned to the correct alternative, was used as the principal measure of performance accuracy. It correlated better than .90 with other, more sophisticated indices of accuracy.