### Grant McDermott

Assistant Professor
Dept. of Economics
University of Oregon

# Climate change & the balance of probabilities

Freeman leaves a comment under an older post, regarding my statement that "[...]there are uncertainties in climate science - as any climate scientist worth his salt will keep stressing - but the balance of probabilities at present are undoubtedly sided with the call to action rather than inaction[...]". Here he is in his own words:
As for the "balance of probabilities". let's do some basic maths.

For us to act to 'do something' about climate change (whatever that means these days) we need to accept the following propositions.

1. The climate is changing
2. The climate is changing in a warming direction.
3. This warming is of a magnitude never before seen
4. This warming is man made
5. This man-made warming costs the planet more than it benefits it and therefore should be reversed
6. This warming can viably and best be reversed by regulatory policy choices
7. This reversal will be enough to reinstate the 'before' state of climate
8. We can stop this reversal process at the 'before' state without it overshooting to an overly cool state and creating other negative costs.

No[w] let's assume, and this is DEFINITELY NOT the case, but let's assume for the sake of the [thought] experiment that each of these propositions could be asserted with 90% confidence. By my simple reckoning that would mean that the decision to intervene by introducing all manner of policies and regulations would need to satisfy a probably criteria for success of 0.90^8 = 0.43.

So even if we were totally (90%+) confident on each of these independent propositions, we still only arrive at roughly a 50/50 call AT BEST. Now, call Mr. Stuck in the Mud, but I would prefer to see a bit more debate on this one before talking about the 'balance of probabilities'. Moreover, I'm surprised you even want to talk about balance of probabilities, because on the numbers I've just run that balance looks rather skewed out of your favour...
Freeman's maths example is interesting and, to be honest, is something that I also considered when first getting involved in this climate debate. Unfortunately, simple probability (geometric) summing as he has done here is not the appropriate measure to use and can lead you to bad conclusions. Let me try to explain why:

If you think about it, you could construct a long enough daisy chain leading up to any trivial future event $$-$$ as Freeman did, applying equal importance to the probability of every sub-outcome $$-$$ to dissolve in a sea of indecision. Should I book that holiday in December when there's a chance that 1) I might get sick, 2) airfares could go down, 3) the plane could crash, 4) another destination might be better, 5) I might have important work to do, 6) I might not like my accommodation, etc, etc?

Of course, we "sense" that there's something wrong with type of logic. So, what's missing?

Basically, you have to weight your propositions according to their relative significance AND then multiply each outcome by their associated costs/benefits. What really matters is the magnitude of the potential risk to society, not simply the risk/probability in of itself. Further, you need to compare the benefits of each potential outcome, rather than the probability of any single outcome by itself. That, after all, is exactly how we deal with standard uncertainty problems in economics.

You could think about it as being the same type of logic that underpins any insurance decision. People don't pay an exorbitant amount for travel insurance, health insurance and car insurance because they think that there is a 90% chance that they will a) get mugged in a foreign city, b) become gravely ill, or c) crash their car in any given month. Rather, we want to insure against these (low probability) risks, because they entail dramatic costs. For the Nassim Taleb fans out there, just think Black Swan events... Thus, even using Freeman's figure of 50/50 should easily be strong enough for most people to spend lots of money in trying to avoid potentially disastrous outcomes.

In the climate change literature, this "fat-tailed" risk (low probability, high impact) has been the specific focus of eminent work by Martin Weitzman, Christian Gollier and others. Actually, on a coincidental note, here's a article that describes Weitzman's work in more depth as a response to flawed criticism by Jim Manzi (who, if you recall, was the subject of my original post under which Freeman was commenting). Warning: It is a bit of tirade against Manzi, who I feel deserves more respect, as indicated by my original post. However, on this issue, I think that he is precisely wrong for the reasons that the author (Joe Romm) points out. Rather than reading the whole article, I'd recommend that you scroll down towards the bottom part, where Romm explains that it is the damages function along the probability distribution function that matters, not the probability distribution (of warming) itself.[*]

Two last points:

Another essential piece that this kind of (static) analysis is missing is that it doesn't consider the likelihood that we will be able to scale up/back our efforts in the instance that we are wrong in our current predictions.[**] According to an overwhelming majority of our best (relevant) scientific experts, it will be considerably easier to prevent a runaway Greenhouse Effect the sooner we begin to do so, due to long-lived nature of CO2, etc. Basically, it is far easier to repeal unnecessary environmental regulations than reverse the forces that drive climate change. (I am happy to debate anyone who argues to the contrary... Any elected official that proposes to keep carbon legislation after it has been disproven as the source of global warming would be committing political suicide.)

Finally, I would also say that I don't fully agree with the sequence (and composition) of Freeman's propositions, nor the probabilities that he ascribes to them. For example: Propositions 1 and 2 (and even 8) are 100% or very close to it, while Proposition 3 is not particularly relevant (since what matters is the experience of modern humans, not dinosaurs). Actually, the leading scientific research on the subject indicates that Propositions 1 through 4 are true with 90% certainty taken together... and not 90^4. So you're already looking at much higher overall probability. Further, Proposition 7 is incorrect since the focus is not necessarily on "no" warming, but rather on what marginal level of warming will bring the greatest net benefit... This, of course, the seminal debate of climate change economics.

Anyway, that last paragraph is really just nit-picking. I know that Freeman presented these propositions as something of a thought exercise more than an absolute set. Nevertheless, I believe that this simple approach is incorrect for the reasons stated above.

[*] Start where it says: "Now I and many others have long argued that traditional cost-benefit analysis doesn’t capture risk posed by the worst-case scenarios. The economist who has most clearly delineated this in Harvard Martin Weitzman[...]"
[**] You could, of course, look to incorporate these by using effective weights...