Applied a theory of information integration to decision making with probabilistic events. 10 undergraduates judged the subjective worth of duplex bets that included independent gain and lose components. The worth of each component was assumed to be the product of a subjective weight that reflected the probability of winning or losing, and the subjective worth of the money to be won or lost. The total worth of the bet was the sum of the worths of the 2 components. Thus, each (...) judgment required multiplying and adding operations. The multiplying model worked quite well in 4 experimental conditions. The adding model showed more serious discrepancies, though these were small in magnitude. The theory of functional measurement was applied to scale the subjective values of the probability and money stimuli. Subjective and objective values were nonlinearly related both for probability and for money. (shrink)

A review of the literature indicates that linear models are frequently used in situations in which decisions are made on the basis of multiple codable inputs. These models are sometimes used normatively to aid the decision maker, as a contrast with the decision maker in the clinical vs statistical controversy, to represent the decision maker "paramorphically" and to "bootstrap" the decision maker by replacing him with his representation. Examination of the contexts in which linear models have been successfully employed indicates (...) that the contexts have the following structural characteristics in common: each input variable has a conditionally monotone relationship with the output; there is error of measurement; and deviations from optimal weighting do not make much practical difference. These characteristics ensure the success of linear models, which are so appropriate in such contexts that random linear models may perform quite well. 4 examples involving the prediction of such codable output variables as GPA and psychiatric diagnosis are analyzed in detail. In all 4 examples, random linear models yield predictions that are superior to those of human judges. (shrink)