## (Not) Falling for the Fallacy

An important concept is demography is the ecological fallacy.  This is where aggregate data for a group are used to draw erroneous inferences about individuals belonging to the group.  The less well known flip side to this is the atomistic fallacy (or individualistic fallacy), where attributes of individuals are used to make incorrect generalisations about the group to which they belong.

A related example of this was illustrated in an earlier posting on the link between smoking propensity and geodemographic type.  In the P2 classification, people in category L were three times more likely to smoke than people in category A.  People in category L therefore tended to have higher mortality and didn't live as long as those in category A.  Of course, this doesn't mean that everybody in L is a smoker, or that everybody in A will outlive them.  Clearly, there will be some long-lived non-smokers in L and some short-lived smokers in A.  In the absence of detailed knowledge of who smokes and who doesn't, geodemographic type acts as a proxy for unobserved health behaviours.

However, proxies have to be used intelligently.  For example, we once came across a cigarette manufacturer looking for a bulk-annuity quotation for the pension scheme.  It was therefore reasonable to suspect that the proportion of smokers was much higher than the (nationally calibrated) geodemographic profiles would suggest.  In another example, a sizeable pension scheme had credible experience data indicating much higher mortality rates than the geodemographic profile suggested.  Upon inspection it was discovered that the company's workforce had a historic exposure to asbestos and high rates of resulting mortality.

Of course, these two examples do not invalidate the use of geodemographic profiles.  In the case of the cigarette manufacturer, geodemographic type can still be used as a proxy for health behaviours besides smoking.  And in the asbestos example, the degree of a pensioner's occupational exposure will likely be strongly correlated with geodemographic profile.  These two cases show the importance of scheme-specific mortality investigations where there is enough data to support them.

Assume we have a random variable, $$X$$, with expected value ... Read more