"Efficiency is intelligent laziness." - Anonymous
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The danger with rejecting broadly true stereotypes is that one tends to be too zealous in rejecting them (this is a problem on top of the base rate fallacy).
When faced with a case that in reality conforms to the stereotype, one will be reluctant to recognise and endorse it. Thus, in the end one is likely to make more wrong evaluations than if one had kept to the stereotype in the first place.
For example, assume that 60% of members of Group A possess Characteristic C. When an Unbiased Observer, UO, observes a group of 100 As, he will correctly assess that 60 of them possess Characteristic C.
Yet, when a Politically Correct Observer, PCO, observes a group of 100 As, in his zeal to avoid discrimination and quell stereotypes he is likely to assess that much fewer than 60 As (say, 20) possess Characteristic C (ie he is wrong 40% of the time, assuming no false negatives).
Hell, even a Biased Observer, who overestimates the veracity of the stereotype, would be more accurate than the PCO with any assessment less than 100%. In other words, even if he assumed that 99 out of 100 As possessed Characteristic C (ie he is wrong 39% of the time, assuming no false negatives), he would be more accurate than the PCO.
[Ed: Keywords to make this easier to find:
Characteristic A
Heuristic
0%
None of them
None of Group A
The population with
The people with
Type A
probability that a
member of group A]