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262 Biases in probability assessment
time, and then anchor on to it. In consequence, the adjustments to the
upper and lower limits of the range are too small to give the stated
probability of including the true value. For example, in a study by
Alpert and Raiffa, 13 subjects were asked to provide estimates of various
quantities in the form of ranges which were to have a 90% probability of
including the true value. In fact, only about 57% of the quantities actually
fell within the estimated ranges. It appears that overconfidence is most
marked when people lack expertise or knowledge about the quantity
they are estimating. People with expertise or relevant knowledge tend
not to be overconfident, and they may even have a tendency to be
underconfident.
As we shall see in Chapter 10, overconfidence is of particular concern
when probability distributions have to be estimated. There is a
danger that when estimating maximum and minimum possible levels
of quantities like costs or sales, decision makers will estimate ranges
which are too narrow to include all of the possibilities. The elicitation
methods which we outline in that chapter are designed to avoid
this problem by (i) discouraging decision makers from anchoring on a
particular quantity and (ii) encouraging them to widen their estimated
range by imagining circumstances where the true quantity might fall
outside it.
Test your judgment: answer to question 14
Q14. Were you overconfident in your estimates? The true values of the
quantities are given below.
(a) 10 118 miles
(b) 97 gold medals
(c) 839 781 square miles
(d) 1938
(e) 1876
(f) 187 000
(g) $105 263 million
(h) 1809
(i) 14 000 feet
(j) 1770 miles.
If your 90% confidence was justified, we would expect nine
of your 10 ranges to include the true value. If fewer of your
ranges achieved this then this suggests that you were overconfident.