A Developmental Research On Subjective Probability Judgment: Based On Random Support Theory

Random Support Theory is a subjective probability judgment calibration theory based on support theory. Via massive judgments research by treating supports as random variables, it can describe and predict calibration properties effectively and explain these properties with several simple psychological model parameters.The validity of Random Support Theory is testified in this paper, and then explored to study the developmental properties of youth subjective probability judgment. The reason of subjective probability judgment miscalibration and the necessary conditions of perfect calibration are also studied later with the model.The youth half-ranged judgment properties are studied in experiment 1 with paired city populations' judgment confidence assignment. Aggregate level analysis shows:Ⅰ. Junior, senior and college participants are all over-confidenced in subjective probability judgment.Ⅱ. Overall accuracy increases with age. Excluded the effect of accuracy on judgment confidence,σis a good measure of the extremity of subjective probability judgment. College people show the highest extremity, followed by junior high group, and senior high group the lowest.Ⅲ. Three groups are significantly different in judgment confidence of whole items, with college group the highest, junior high lower and senior high the lowest.Ⅳ. The correlations of judgment and accuracy made by three groups are all positive, which shows the ability of youth people to make reasonable subjective probability judgment. However, these correlations stand only when items are natural samples of related field. Specifically, single item or all items which have an above 50% accuracy show judgment confidence-accuracy positive correlations, and which have a below 50% accuracy show judgment confidence-accuracy negative correlations. Both effects are explained by Random Support Theory.Ⅴ. Calibration curves and response proportions of all three groups are predicted greatly by Random Support Theory, which at the same time explains the different calibration properties among the three groups.Item analysis is interested in the relationship of single item average judged probability and accuracy, which shows:Ⅰ. Those items which have an above 50% accuracy show average judged probability-accuracy positive correlations and those below 50% show negative correlations.Ⅱ.With extremity parameterσheld persistent, model predicts and verifies the hard-easy effects in junior, senior and college groups convincingly.In order to figure out the real reason of miscalibration with Random Support Theory, experiment 2 basically repeat the research made in 2005 by Brenner et al., which shows: Random Support Theory greatly predicts calibration curves under four class conditions(2 base rates×2 diagnosticities) And explains the reasons of all calibration properties. At the same time, what is confirmed is that over-confidence is only a byproduct of case-based judgment but a native humanity.Experiment 3 is based on experiment 2 to find out the necessary class property required by perfect calibration. Results show: Focal bias parameterβis not all about base rate of focal hypothesis. A part of it has nothing to do with the base rate but affected by judge's motive factor, thus, positive or negative skewed. 50% is by no means a necessary base rate required by perfect calibration.β' is positive, the required base rate is above 50%; negative, below 50%.β' is a measure of focal hypothesis content favor.