Some time ago, Stephan Lewandowsky wrote an article on planet3.0 "
The Inescapable Implication of Uncertainty" (also
available on his own blog as part of a series), which made the fairly straightforward point that the expected cost of climate change is greater as a result of uncertainty about its magnitude (eg, the canonical example of climate sensitivity), and thus those who argue that uncertainty is a justification for inaction are precisely backwards in their thinking.
It's a pretty simple point, which has been talked about by Michael Tobis for a long time. And it's not at all controversial, scientifically speaking. So I didn't think it needing commenting on.
The crux of Stephan's argument is quite simple. The cost of climate change is generally considered to be a nonlinear (
concave convex - see comments) function of the magnitude of warming. This is a standard result of all attempts at economic modelling that I am aware of, and in my opinion is very intuitive and natural. For example, I used the quadratic function C(T) = 0.284T
2 (where T is temperature change, and the cost is expressed as % GDP loss) in our
Climatic Change paper (available
here). This function was directly based on the DICE model of Nordhaus. AIUI all credible economic modelling generates qualitatively similar results. (Incidentally, it doesn't affect the argument in any way at all if the loss function actually has an optimum at some nonzero temperature change, as some others have found.)
The point about a concave convex function - indeed it's (almost) the very definition of concave convex - is that for any small t, (C(T+t)+C(T-t))/2 > C(T). Or in words, the average of the costs of T+t and T-t is greater than the cost of T. The consequence of this is that symmetric uncertainty about the value of T leads to an increase in expected cost, compared to a deterministic outcome.
The application to climate change is straightforward, as illustrated with the following simple example. If we know that the sensitivity is 3C (say), then the cost function based on the DICE model gives a ultimate loss of 2.6% GDP for a highly simplistic scenario in which CO2 doubles and is then held constant. If instead of a known sensitivity of 3C, we thought the sensitivity might equiprobably be 2C or 4C, then even though the mean value (our expectation of the temperature change) is unchanged at 3C, the expected cost is (1.1+4.5)/2 = 2.8% GDP. For a 50-50 chance of either 1C or 5C, the expected cost rises to (0.3+7.1)/2 = 3.7%, and for 0C or 6C it's 10.2/2 = 5.1%. The discerning reader may have noticed the first hints of a pattern here...
Another way of saying it, is that the expected cost of (uncertain) climate change is greater than the cost of the expected climate change. (This is using the concept of expectation in the mathematical sense - note that in the uncertain case, there is no possibility of the cost actually being 2.8%, it will either be 1.1 or 4.5, and we don't know which.) The result is not specific to the particular example, of course, but applies widely. Increasing uncertainty (for any sensible definition of "increasing uncertainty") will generally lead to an increase in the expected cost.
So what's Ben Pile so worked up about? He accuses Stephan of producing "the most remarkable attempt to formulate — or reformulate — the precautionary principle I have ever seen", describes it as "an incredibly tortured attempted to alternate between word play and maths abuse". There's more:
"Lewandowsky, over the course of three posts – one, two, three — reinvents the precautionary principle without ever calling it the precautionary principle. This is interesting in itself… An academic
in the field of climate policy has forgotten that the precautionary
principle already exists, is already applied to the science, and is
already manifested in policy. "
And there's plenty more vacuous hyperbole where that came from.
Unfortunately, Pile is dead wrong. Lewandowsky's argument has nothing to do with the
precautionary principle, so it's hardly surprising that he doesn't mention it. Instead, it's just a simple application of standard economic analysis under uncertainty, which is implicit in all academic work in this area. It was certainly implicit in our Climatic Change paper - I didn't think it worth specifically highlighting in that work precisely because it is so elementary and well known. But Pile has got such a bee in his bonnet about the PP that he doesn't even realise that Lewandowsky isn't even using it. It's a bit odd, because from what I recall of previous posts of Pile's, they are usually fairly sensible (I'm not an avid follower though). But of course it is hardly the first time that a social scientist has blundered into a debate and a made fool of himself though not having the requisite (albeit rather minimal) mathematical skills to understand the issues...