How much should we pay to avoid the tiny risk of total destruction?

How much should we pay to prevent the tiny probability of human civilization collapsing? That is the question at the center of an esoteric debate over the application of cost-benefit analysis to man-made climate change. Harvard University economist Martin Weitzman raised the issue by putting forth a Dismal Theorem arguing that some consequences, however unlikely, would be so disastrous that cost-benefit analysis should not apply.

The danger, according to Weltzman, lurks at the tails of risk probability distribution. The most common probability distribution is the famous "bell curve." In a normal distribution, about two-thirds of values are within about one standard deviation of the mean. For example, among American males the average height is 5 feet 9 inches, and one standard deviation is about 3 inches. This means that two-thirds of American men are between 5 feet 6 inches and 6 feet in height. 95 percent of men fall within two standard deviations - between 5 feet 3 inches and 6 feet 3 inches - and 99 percent are within three standard deviations.

So there's a 99 percent chance that the next guy you see walking down the street will stand over 5 feet and under 6 feet 6 inches in height. As one moves further and further from the mean height, one finds fewer and fewer men who are outside the ever widening height criteria. The probability that you will meet a man who is over 12 feet tall (26 standard deviations from the mean) is essentially nil.

Climate computer models try to estimate future temperatures given the accumulation of greenhouse gases in the atmosphere. In 2007, the United Nations Intergovernmental Panel on Climate Change's (IPCC) Fourth Assessment Report (4AR) estimated that increases in average global temperature for the next 100 years will fall within a likely range of 1.1 to 6.4 degrees Celsius. An increase of 6.4 degrees would be bad enough, but what if it was too low?

In fact, Weitzman contends that the uncertainties surrounding future man-made climate change are so great that there is some probability that total catastrophe will strike. Statisticians often refer to the extreme right-hand and left-hand sides of a bell-shaped probability distribution as its "tails." In the case of adult male height, the tails eventually go to zero - in other words, there are no adult males under 21 inches tall (17 standard deviations) and none over 9 feet tall (14 standard deviations). Weitzman argues that the probability distribution of high-impact low-probability climate catastrophes has a built-in tendency to be fat tailed: Their tails never fall to zero. His claim is somewhat analogous to arguing that the probability distribution for future temperatures never completely rules out the possibility of meeting the moral equivalent of a 12 foot tall man.

Weitzman focuses on equilibrium climate sensitivity. Climate sensitivity is defined as the global average surface warming that follows a doubling of atmospheric carbon dioxide concentrations. The IPCC 4AR finds that climate sensitivity is "likely to be in the range 2 to 4.5 degrees Celsius with a best estimate of 3 degrees, and is very unlikely to be less than 1.5 degrees. Values substantially higher than 4.5 degrees Celsius cannot be excluded." Without going into detail, Weitzman assumes that uncertainties over values higher than 4.5 degrees Celsius can yield fat tails of catastrophic climate change.

Consequently, Weitzman spins out scenarios in which there could be a 5 percent chance that global average temperature rises by 10 degrees Celsius (20 degrees Fahrenheit) by 2200 and a 1 percent chance that it rises by 20 degrees Celsius (36 degrees Fahrenheit). Considering that the globe's average temperature is now about 15 degrees Celsius (59 degrees Fahrenheit), such massive increases would utterly transform the world and likely wreck civilization. Surely people should just throw out cost-benefit analysis and pay the necessary trillions of dollars to avert this dire possibility, right?

Then again, perhaps Weitzman is premature in declaring the death of cost-benefit analysis. Yale University economist William Nordhaus certainly thinks so and has written a persuasive critique of Weitzman's dismal conclusions. First, Nordhaus notes that Weitzman assumes that societies are so risk averse that they would be willing to spend unlimited amounts of money to avert the infinitesimal probability that civilization will be destroyed. Nordhaus then shows that Weitzman's dismal theorem implies that the world would be willing to spend $10 trillion to prevent a one-in-100 billion chance of being hit by an asteroid. But people do not spend such vast sums in order to avoid low probability catastrophic risks. For example, humanity spends perhaps $4 million annually to find and track possibly dangerous asteroids.

Nordhaus also notes that catastrophic climate change is not the only thing we might worry about. Other low probability civilization destroying risks include "biotechnology, strangelets, runaway computer systems, nuclear proliferation, rogue weeds and bugs, nanotechnology, emerging tropical diseases, alien invaders, asteroids, enslavement by advanced robots, and so on." As Nordhaus adds, "Like global warming, all of these have deep uncertainty - indeed, they may have greater uncertainty because there are fewer well-understood constants in the biological and technological world than in the geophysical world. So, if we accept the Dismal Theorem, we would probably dissolve in a sea of anxiety at the prospect of the infinity of infinitely bad outcomes." If we applied Weitzman's analysis to our individual lives, none of us would ever get out of bed for fear of dying from a slip in the shower or a car accident on the way to work.

Weitzman's analysis also assumes that humanity will not have the time to learn about any impending catastrophic impacts from global warming. But mid-course corrections are possible with climate change. People would notice if the average temperature began to increase rapidly, for example, and would act to counteract it by cutting emissions, deploying low-carbon technologies, or even engaging in geo-engineering. And while other low probability calamities, such as the entire Earth being transformed into strange matter by strangelets produced in high energy physics experiments, don't allow for learning, "there is no point in revising our views about strangelets in the microsecond after we discover that the calculations of the physicists are wrong." And yet, we do not shut down such experiments.

On the crucial issue of climate sensitivity, climate researcher James Annan at Japan's Frontier Research Center for Global Change asks if the uncertainties Weitzman talks about aren't just a reflection of our current ignorance, rather than some inherent feature in the climate system itself. Isn't climate sensitivity an imprecisely known constant about which climate scientists can learn more, eventually converging toward a point estimate? If climate sensitivity turned out to be low, that would mean that future climate disasters were less likely. So instead of spending vast sums of money to cut carbon dioxide emissions, a better strategy would be fund research that aims to more closely specify climate sensitivity.

At the end of his critique of Weitzman's Dismal Theorem, Nordhaus investigates what combination of factors would actually produce a real climate catastrophe. He defines a catastrophic outcome as one in which world per capita consumption declines by at least 50 percent below current levels. Since output is projected to grow substantially over the coming century, this implies a decline that is at least 90 percent below the projected baseline. In contrast, the most extreme climate scenario presented by the gloomy Stern Review had people living in 2200 making do with only 9 times current per capital consumption instead of 13 times current consumption.

Nordhaus ran a number of scenarios through the Dynamic Integrated Model of Climate and Economics (DICE), his integrated assessment model. Integrated assessment models like DICE combine scientific and socio-economic aspects of climate change to assess policy options for climate change control. DICE would produce a catastrophic result only if temperature sensitivity was at 10 degrees Celsius, economic damage occurred rapidly at a tipping point of 3 degrees Celsius, and nobody took any action to prevent the catastrophic chain of events. Interestingly, even when setting all of the physical and damage parameters to extreme values, humanity still had 80 years to cut emissions by 100 percent in order to avoid disaster.

Finally, in his 2008 book, A Question of Balance: Weighing the Options on Global Warming Policies, Nordhaus shares the results of running the cost-benefit analysis through the DICE-2007 model. He found that the optimal policy trajectory is one where the world gradually increases the price of emitting carbon dioxide over the next century at a rate in real terms of 2 to 3 percent per year. Nordhaus concludes that the world should impose a tax of $27 per ton of carbon (or $7.40 per ton of carbon dioxide since burning 1 ton of carbon produces 3.67 tons of carbon dioxide). This tax is equivalent to about 9 cents per gallon of gasoline and 1 cent per kilowatt hour of electricity. The tax should increase to $90 per ton by 2050 and $200 per ton in 2100.

Following this carbon price trajectory, the DICE-2007 model estimates that carbon dioxide emissions would be cut 25 percent from what they would otherwise have been in 2050 and be 45 percent lower than otherwise in 2100. The result would be an increase in global mean temperature relative to today of 1.9 degrees Celsius for 2100 and 2.7 degrees Celsius for 2200.

Finally, the question must be asked: Why hasn't anyone ever done an analysis of the fat tailed probability that bad government policy will cause a civilization wrecking catastrophe?

Ronald Bailey is Reason magazine's science correspondent. His book Liberation Biology: The Scientific and Moral Case for the Biotech Revolution is now available from Prometheus Books.