The IPAT equation (environmental Impact = Population * Affluence * Technology) has another weakness that is derived, yet different, from its presentation as a simple multiplication of three terms. To present as a simple multiplication, it needs simple operands. Simplifying those operands eases the pedagogical task, but it also destroys critical information.
If, to determine the environmental impact of some scenario or society, you need to determine population, affluence and technology, then affluence and technology must be stated as averages within the subject population. There’s no need to strike an average on population, of course – it’s inherently an aggregation. But within that population, affluence and technology are bound to vary. Some folks are more affluent, some less. Some use technology A, others technology B. For each specific individual, a specific pairing of affluence and technology applies [presume, for now, that “affluence” and ”technology” are each uni-dimensional). To apply affluence and technology factors across an aggregate population, thus, A and T must each somehow be averaged.
But by averaging affluence and technology, we implicitly assume that all members of the population operate identically which, in any real-world population, is false. We fall into an ecological fallacy. We create the impression that, were one person to be subtracted from the population, it wouldn’t much matter which one. But in the real world, subtracting (or adding) one individual to a non-homogeneous population doesn’t always create the same delta environmental impact. Those who, as individuals, enjoy more affluence or use less efficient technologies (again, presume that those terms describe things that can be measured uni-dimensionally) create bigger impact deltas than others.
The use of averages isn’t a harmless methodological simplification, it destroys meaningful information. Of course, the destruction gets more significant as the populations in question get larger and more heterogeneous and, in my experience, students tend to think of IPAT in terms of national or global populations – extremely large and homogeneous. I fear that information loss by averaging makes the IPAT equation more comfortable for students. If environmental impact is a product of averages, then not only are we all equally in the same environmental situation, we’re all in an environmental situation that we all equally created. Nobody’s more or less to blame than anyone else and, since none of us can move the average significantly on an individual basis, our individual behaviors aren’t the root cause of anything. Mistakes may have been made, but change becomes less emotionally imperative.
In addition to changing IPAT from a simple multiplication to a more complex (if still calculable) mathematical function, then, we need to change it from an expression in three discrete variables to one which operates on sets of individual values. We can do that without losing IPAT’s conceptual validity by making Affluence and Technology not averages but summations or – better – integrations. Population is still an aggregate, but the identity of individuals within that aggregate need not be masked. Affluence and Technology can be depicted in ∑ or ∫ notation, thus retaining reference to whole sets of values. And maintaining the ability to ascribe impacts to individual behaviors.
None of which, of course, yet gets to the question of whether affluence and technology are, in fact, uni-dimensional. Nor whether they’re even independent variables at all.