Sunday, December 13, 2009

Pascal's Wager and Climate Change (Revised)

Current climate science suggests that the Earth's temperature has been steadily rising due to greenhouse gas (GHG) emissions produced by our use of fossil fuels such as coal, oil, and gas, and that the rate at which are pumping CO2 and other gases into the atmosphere exceeds the ability of the oceans and the plants to absorb them. If GHG emissions continue unabated then, scientists predict that the Earth's average temperature will continue to rise, and this may cause some potentially very serious climatic changes such as melting glaciers and icecaps, rise in sea levels, species displacement and extinction, spread of tropical diseases, refugee flows, droughts, floods, increasingly powerful cyclones, and so forth.

While there is a strong consensus among climate scientists that the theory of anthropocentric (human-induced) global warming is true with a high degree of certainty, a great many people still refuse to believe it. Some of these skeptics are suspicious of the explanation that humans burning fossil fuels is the cause of the warming trend and point out the existence of some studies that cast doubt on the consensus view (Alexander Cockburn claims the theory is a farce) . The recent release of "climate gate" emails from scientists at the University of East Anglia's Climatic Research Unit suggesting that they had tailored some data to fit this theory fueled climate change skeptics and deniers. Recent Polls show that the percentage of Americans who believe in anthropogenic global warming has declined. Some climate skeptics believe that the whole story is a hoax concocted by a vast left-wing conspiracy. Many of these climate skeptics are also vehemently opposed to the world's nations taking any serious steps to reduce GHG emissions in order to mitigate the threats predicted to arise due to global warming by reducing the use of fossil fuels and moving rapidly to a carbon-neutral energy economy.

But the question about whether or not we should now take serious steps to reduce GHG emissions is a classic case of decision-making under uncertainty. The question whether we should believe or disbelieve in current climate science is analogous to Pascal's Wager, named for the mathematician and philosopher Blaise Pascal (1623-1662) whose Pensées contained the following intriguing paragraph:

“God is, or He is not.” But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up... Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose... But your happiness? Let us weigh the gain and the loss in wagering that God is... If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.

In this argument Pascal portrays the decision about whether to believe in God or not as a wager made under conditions of uncertainty. In modern decision theory the logic of his argument is represented by a decision matrix such as the following:


God exists (G)God does not exist (~G)
Believe God exists (B) eternal heavenly bliss
-N (none)
Not Believe God exists (~B) eternal damnation or (perhaps) purgatory

+N (none)

His argument suggests that if God exists, the reward for believing that God exists is very high, whereas the cost of not believing in God (if indeed He does exist) is very great --- eternal damnation. Therefore, it is a good bet to believe in God. If, on the other hand, it turns out that God does not exist, then the benefits as well as the costs are negligible (perhaps some Sunday mornings wasted going to Church), and perhaps, if God does not exist, we will never really know anyway whether our bet paid off.


Philosophers have found various reasons to object to this argument as providing a good basis for theism. But I leave these philosophical niceties aside, interested readers might want to consult the article on Pascal's Wager in the Stanford Encyclopedia of Philosophy. My intention here is to suggest that there is a similar (and much better) argument to be made about the uncertainty of catastrophic climate change due to anthropogenic (human-induced) changes in the concentration of CO2 and other greenhouse gases in the Earth' atmosphere.


There will be a big payoff if we believe in current climate science and take steps to reduce carbon emissions, and it turns out the theory was correct. And there will also be a big loss if we do not believe in current climate science, when it turns out that the theory was correct -- oops, we cooked the planet. Assuming that there is a greater than zero chance that current climate science is correct, then the rational wager would be to accept it and act so as to gain the best outcome and avoid the worst one, even if there remain some doubts about whether the current science is indeed correct. As a decision matrix this set of choices would be represented like this:



Current Climate Science is correct (C)
Climate Science is not correct (~C)
We believe in climate science and act (B)
F1
F2
We do not believe in climate science and do not act (~B)
F3
F4


What are the relative values of F1...F4 in this payoff matrix? In order to make the answers more concrete suppose that you will be able to experience the planet Earth as it will exist 100 years from now. Perhaps you will still be alive because of miraculous new lifespan enhancing medical technologies. Or if you prefer a more supernatural possibility, suppose that you do die but will be reincarnated as one of your own great great grandchildren, or as another member of their generation.

Let's first examine the value of F3. If we do not believe in current climate science and act (~B) to mitigate its predicted catastrophic effects by rapidly transforming our energy economy so as to radically reduce GHG emissions, and it turns out that the current science is correct (C) in predicting catastrophic climate changes 100 years from now if we do not act, then you or your great great grandchildren will be very unhappy campers on Planet Earth. The payoff value of F3 (~B & C) is strongly negative. How would you feel about F3? Well probably a lot like an atheist who dies and meets St. Peter at the Pearly Gates --"Oops, I guess I was wrong, Gulp!"

What then is the value of F1? In this case, we decided to believe in current climate science and acted in order to mitigate its worst predicted effects, and it turned out that our current theories were indeed correct (B & C). The payoff for F1 is then very high indeed. F1 is analogous to the situation of the faithful religious believers who discover that the God they accepted does indeed exist, except that their reward is an earthly one, a planet whose climate is not greatly altered and disrupted by human activities.

So, just looking at these two values F1 and F3, we can say that F1 dominates F3, that is, that the expected utility of believing in climate change is far greater than the expected utility of not believing in it. Therefore, even with uncertainty about C, it is rational to bet that current climate science is correct and take steps now to significantly reduce our GHG emissions.

But we must also consider the costs and benefits of F2 and F4, the cases where current climate science is not correct. Suppose that in 100 years we learn that the climate science of the early 21st century was wrong in predicting catastrophic climatic changes due to anthropogenic GHG emissions (~C), but because people in the early 21st century believed in it (B) they spent a lot of money and effort on energy efficiency, electric cars, windmills, solar panels, and hydrogen fuels cells, and all that green stuff. How would you feel about that? I guess you would probably feel pretty okay about it; it would be kind of like learning that you had already been saved through God's grace, and it really didn't matter whether you went to church or not, even though you did. But your ancestors did make a big effort to "Go Green" for nothing, so let's say that F2 is marginally negative.

Now, finally, for F4 suppose that at the present we do nothing to prevent further increases in global temperature by altering our current fossil fuel energy economy (the so-called "business as usual" scenario), but that it turns out that current climate science is wrong, and nothing very bad happens. This is like finding one has a "Get into Heaven Free" card even though one lived a life of sin. One can imagine this would make one pretty happy. So let's say F4 is marginally positive.

Since F1 and F2 together still yield a strongly positive payoff, while F3 and F4 still yield a strongly negative one, it is still rational to bet that current climate science is correct and act on that belief.

Critics of this argument may want to quibble with my estimate of the cost of F2. Climate skeptics are likely to argue that the cost of mitigating global warming is going to be greater than marginally negative. We will have to make some real sacrifices in order to reduce our GHG emissions to safe levels by mid-century. Let's assume this is correct. Even so, it is worth it because the expected loss if we do nothing is too great. As the authors of a recent report on the economics of climate change argue, it is also possible to think of the choice we face as analogous to the decision to buy fire insurance:
The reason people buy fire insurance is not because they are certain that their house will burn down; rather it is because they cannot be sufficiently certain that it will not burn down. Likewise, the projections of dangerous climate risk if the world exceeds 350 ppm CO2 in the long run are not certainties; they are, on the contrary, necessarily uncertain. If the worst happens our grandchildren will inherit a degraded Earth that will not support anything like the life that we have enjoyed. On the other hand, if we prepare for the worst, but it does not happen, we will have invested more than, in perfect hindsight, was necessary in clean energy, conservation, and carbon-free technologies. How would we feel about discovering we had done too much about climate change, compared to discovering that we had done too little? (DeCario, S.J., Norgaard, R .B, Norman, C. S., and Sheeran, K.A. "The Economics of 350: The Benefits and Costs of Climate Stabilization." Economics for Equity and Environment. www.e3network.org. October 2009, p. 6.)

So how much is catastrophic climate change insurance going to cost? According to this study, which is based on a comparable analysis of several economic projections done both by business-sponsored groups, and nongovernmental and academic groups, it is estimated that climate insurance would cost between 1% and 3% of global GDP in order to reach the lowest carbon target currently being discussed, 350 ppm. As the authors of this report reckon:
Suppose the cost of climate protection turns out to be 2.5% of global GDP, toward the high end of the global scenarios just discussed. In an economy that is growing at 2.5% per year, a rate that is common for developed countries, spending 2.5% of GDP on climate protection each year would be equivalent to skipping one year's growth, and then resuming. Average incomes would take 29 years to double from today's level, compared to 28 in the absence of climate costs. In an economy experiencing 10 percent annual growth, as China has in many recent years, imposing a cost of 2.5% per year is equivalent to skipping 3 months of growth; if 10% growth is sustained, average incomes would reach twice the current level in 86 months, compared to 83 months in the absence of climate costs.
In fact, these authors argue that at the early stages of a climate mitigation program we might actually save money because we are reaping the benefits of greater energy efficiencies. But the bottom line conclusion derived from this study is that, "There are no reasonable studies that say that a 350 ppm stabilization target will destroy the economy; there are no studies that claim that it is desirable to wait before taking action on climate protection" If this is correct, then buying climate insurance is a good investment because we can easily afford it and with a relatively modest cost we can avert a disaster in the making.

On the other hand, if we disbelieve in current climate science and do nothing now to reduce our carbon emissions, then either we discover that we spent 1%-3% of global GDP converting to a carbon-neutral energy earlier than we had to, or we find that we overheated the Earth and our house burned down.

So you climate change skeptics and deniers out there, which risk would you rather take? Would you rather that we now take steps to prevent catastrophic climate change when we can easily afford climate insurance, or do you want to go on business as usual without spending anything on insurance and risk the catastrophic climate changes that current science is predicting? You must choose now. Choose wisely.