Thursday, June 9, 2011

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...


  1. Thanks for the clear thoughts on this stickman. Good points raised. My objection here (although not going to flog it as I am completely pooped out by our previous exchanges!) is that a lot of the estimation of the "damages function" to my mind is open to huge (and I mean HUGE) margins of error and may often be downright hypothetical 'what ifs' rather than scientific endeavour (this is not to say scientists aren't trying to make it as scientific as possible).

    I agree with you on my 3rd proposition, which would be a less important subset of sorts to proposition 5.

    As far as proposition 8 being close to 100% is concerned, I find that highly implausible, but don't know enough about the science in this area to comment further. Proposition 1 is exactly 100% I would say:) but with 2 I think there is enough doubt to make a near-100% assertion 'overly confident'. Please bear in mind that by proposition 2 I'm asserting not just a short term warming trend (which even that I think is tenuous as NASA had to admit), but a structural secular long term warming trend (even less easy to be confident about).

    Proposition 5 and 6 are most interesting to me. I would assume that you would give proposition 6 a high probability, although it being in the realm of trying to prove something we've never achieved before in a system of almost infinite complexity suggests to me that confidence levels anywhere above 50-60% would be wishful thinking (complete gut feel).

    As far as 5 is concerned, and I admittedly am not well read enough on the science, my feeling is that much more needs to be done in terms of the benefits of global warming. My fear is that these benefits are not taken seriously enough in study by scientists with 'warming goggles' on who want to demonstrate a coming crisis. Just exploring the agricultural possibilities of a much smaller arctic circle, or greater possibilities for more diverse biomes over larger areas of the planet, or MUCH less fossil fuel use for heating purposes are just a smattering of the kind of 'benefits' research that needs to be done.

    The cost-benefit analysis would need to COMPREHENSIVELY assess potential costs and benefits plus layer over this the cost of economic regulation in taking the remedial action. I'm sure these analytical attempts have been made, I just wonder somewhat pessimistically if this is even possible with any serious degree of accuracy, and I also suspect the benefits of a warmer planet have been under-represented in the academic literature.

    This by the way would also dovetail into your damages function analysis and possibly yield far less catastrophic 'potential' outcomes in climate model scenarios based on the benefits offset.

    When we next meet over a beer at La Med (whenever that may be!) we can chat lekker about all this:)

    Take care mate

  2. Thanks bud,

    While I'm obviously stoked that you find some value in the way that I've explained this "probabilities" issue, you again raise a number of important aspects that are all incredibly relevant to the climate debate. In that light, I suppose that I can do no better than to say that, yes, climate scientists (and economists) are actively engaged in accounting for all issues that you raise.

    For instance, on the benefits of Global Warming, there is an extensive literature aimed at assessing the relative winners and losers in a geographic sense.
    - E.g. With respect to agriculture, current research suggests that parts of the US will strongly benefit from mild, 1-2 degrees, warming in terms of crop yields. Africa, on the other hand, stands to be a big loser.
    - Another example, I've read a number of papers that look to assess the relative impacts of warming on energy demand in Europe. The central result is again that some countries will benefit from reduced energy costs (largely in the North), while others lose (in the South).

    On the aggregate though, the planetary negatives outweigh the benefits. Of course, there remain uncertainties, but again I interpret this as a call for caution given that the predicted risks are heavy on the upside.

    The central repository for all this information is, of course, still the IPCC. I would say that too few people make use of this resource, particular given that it's all publicly available information. I find it pretty accessible, so take a look!

    My favourite climate science website, however, is Skeptical Science. The format is brilliant (e.g. the "beginner", "intermediate" and "advanced" tabs) and I know that it helped me get a handle on how much stock to put in many avenues of scepticism/criticism of climate science.

    This is obviously a hugely complex issue, with so many contradictory sources of information. My own believe is that people's position on climate change will undergo something of a U-shaped curve. You likely start off believing that man-made warming is happening after hearing the basic results of the govts, IPCC and so on. However, you then start to question all of this after coming across seemingly endless lines of (apparently valid) criticism. Nevertheless, if you persist and scratch a little deeper, you find that this criticism is largely bogus and/or already accounted for... And that brings you up for fresh air on the other side :)

    Most importantly though: I'll see you on that beer and raise you another! Hoping to make it back to SA in Oct for Becks' wedding so will keep you chaps informed. Cheers pal.

    [Side note: Yes, amazing how tiring these internet debates can be! As usual xkcd knoweth all.]

  3. Concerning the "fat tailed risk", is there for some reason not a fat tailed risk to the kind of policies that would prevent global warming? I don't think anyone disagrees that government's have caused many horrors with a lot weaker justification. Consider an extreme example that Hitler's justification of killing was the coming good shortages.

    Similar neglect is given to the fat tailed risk of preventing terrorism. For some reason, the fat tailed risk is always on the policy governments are trying to prevent, and not applied to the preventative policy itself.

    1. For the Hitler reference, see Mein Kampf chapter 4.