The average probability estimate of J > 1 judges is generally better than i
ts components. Two studies test 3 predictions regarding averaging that foll
ow from theorems based on a cognitive model of the judges and idealizations
of the judgment situation. Prediction 1 is that the average of conditional
ly pairwise independent estimates will be highly diagnostic, and Prediction
2 is that the average of dependent estimates (differing only by independen
t error terms) may be well calibrated. Prediction 3 contrasts between- and
within-subject averaging. Results demonstrate the predictions' robustness b
y showing the extent to which they hold as the information conditions depar
t from the ideal and as J increases. Practical consequences are that (a) su
bstantial improvement can be obtained with as few as 2-6 judges and (b) the
decision maker can estimate the nature of the expected improvement by cons
idering the information conditions.