Coherence of human judgment in a limited probabilistic environment

Abstract

The extent to which human subjects can handle a limited probabilistic task environment is studied. The basic question concerns the existence of an internal representation of probability distributions of heights of men and women, accessible through different response-modes. Forty-eight subjects estimated each probability distribution separately (1) by giving percentiles of the cumulative distribution and (2) through probability estimates on pairs of discrete height intervals. From these two sets of estimates, values were inferred for p(m) i: the probability that a person is a man, m, given the person's height, i. This probability was also (3) directly estimated. Half of the subjects participated in a fair betting game during probability estimation. All subjects were trained in the operational meaning of the probability concept. Direct estimates of p(m) i agreed well with values inferred from individual percentile estimates. Values inferred from the more difficult probability estimates on pairs of intervals, however, showed a strong central tendency effect. Significant correlations in performance among the three response-modes indicated that the latter consistently reflect individual differences in conservatism/radicalism. No effect was observed of participation in the betting game. The results are discussed in relation to the concept of subjective sampling distributions, which is sometimes used to explain accuracy variations in binomial and multinomial inference tasks. It is hypothesized that subjects, through experience and understanding, acquire an internal representation of the task environment. This representation can be put to use in some desired form only if a proper response-device is sufficiently well understood so that it makes the information accessible. The quality of the representation determines whether sets of responses can be given for which normative models from probability theory do or do not hold.