Possible price of fossil fuels (arbitrary units)
Human-induced climate change is a classic case of Hardin's tragedy of the commons — the benefits of burning fossil fuels accrue to individuals, companies and nations, whilst the costs accrue to the planet as a whole. The tragedy of the commons is essentially a multi-player generalization of the prisoner's dilemma. Using a gene-based biological approach, Salter (2003) estimates the relative investment that individuals allocate to their self, offspring, ethny and humanity. The table below shows that individuals are motivated to invest something like 3% of their resources into humanity as a whole (the numbers are merely indicative). This does not bode well for voluntary mitigation of climate change.
| self | 0.7 |
| offspring | 0.2 |
| ethny | 0.07 |
| humanity | 0.03 |
The surest way for a country with a given population to increase wealth is to implement a free market, so the concept of a free market is a good thing. However, there is a catch: markets do not take into account externalities (effects of transactions that affect third parties). Greenhouse gases are an externality, so in order to prevent 'cheating', we must deal with greenhouse gases via government intervention. We are bad at looking for altruism, but good at detecting cheating (Cosmides 1989). Broadly speaking, there are three approaches to dealing with the problem of global waming: adaptation, mitigation and geoengineering. Two popular solutions are a carbon tax and emissions trading (cap and trade). They are theoretically equivalent except that they're logically opposed regarding where the uncertainty lies: a carbon tax fixes the rate of taxation and allows emissions to vary, whilst emissions trading fixes emissions and allows the cost of compliance to vary. Tax or trade? One solution is tax and trade. If we generalize both of them, the regulator allocates an initial fixed quantity of permits, but may engage in trading of the permits, buying them back or selling more. The regulator is then free to vary both emissions and the cost of compliance. If the regulator does not engage in trading, he has fixed the emissions. If he sells an unlimited number of permits at a fixed price, he has fixed the cost of compliance. In other words, we have the best of both worlds. The regulator can choose to what extent both emissions and cost of complinace vary. The four possible scenarios are outlined in the table below.
| The regulator sells a fixed number of permits at a fixed price. | The regulator sells a fixed number of permits at a variable price. |
| The regulator sells any number of permits at a fixed price. | The regulator sells any number of permits at a variable price. |
The problem of global warming is both mitigated and complicated by the fact that fossil fuels are running out. Oil is expected to last another 43 years, gas 167 years and coal 417 years. See the table and charts below. I fitted the Hubbert curve for fossil fuel production, and the inverse for price. The latter is quite arbitrary. The issue is both political and time-sensitive: if those countries that burn fossil fuel the most efficiently cut back, more of the remaining fossil fuels will be used up by those countries who burn fuel less efficiently. If we wish to build a model and perform a cost-benefit analysis, we need to decide the relative importance of the current population and the populations in the future. How do we determine the social discount rate? This is a moral judgement, and morality is a product of the gene-centred evolutionary forces which shape human social psychology. Although our ultimate motivation is gene propagation (long term), our proximate motivation is sex and to care for our kin (short term). In other words, we have evolved on a need-to-know basis, and we care only about our living relatives (the immediate future). On this basis, should the social discount rate for 100 years time or more be 0% or 100%? A minority of people deceive themselves into helping to solve our ultimate goal on a global basis, enabling propagation of our genes and everyone else's (aka saving the world), because this helps them achieve their proximate goal, via their enhanced status, of sex. Although the world often seems to be speeding up, foresight still pays off. Parts of the London Underground system that are still in use were built in the 1860s, and today's engineers are facing projects the lifetime of which will extend to 2100.
| Peak in production | Expected to 'run out' | |
|---|---|---|
| Oil | 2007 | 2052 |
| Gas | 2025 | 2176 |
| Coal | 2028 | 2426 |
Source: Wikipedia (2009)
Fossil fuel production
Possible price of fossil fuels (arbitrary units)
| Greenhouse gas | Chemical formula | Preindustrial level | Current level | Longetivity in troposphere | |
|---|---|---|---|---|---|
| Water vapour | H2O | 36-70% | |||
| Carbon dioxide | CO2 | 9-26% | 278ppm | 379ppm | > 100 years |
| Methane | CH4 | 4-9% | 700ppb | 1774ppb | < 10 years |
| Nitrous oxide | N2O | 275ppb | 319ppb | 100 years | |
| Ozone | O3 | 3-7% | a few days | ||
| CFCs | various | 0 | 0.707ppb |
Sources: Henson (2008), Maslin (2009), Wikipedia (2009)
Climate change is subject to both positive and negative feedback. As an example of positive feedback, as carbon dioxide increases and warms the planet, the atmosphere is able to hold more water vapour, which itself is a greenhouse gas.
How do we encourage the behaviour we desire? Communication is more important than punishment. It is important to be--and let others be--aware that climate sceptics tend to cherry pick data. Have you heard the story about the fact that the earth has been cooling since 1998? If you look at a graph, you will see that 1998 was a high outlier, and that the long-term trend is still up. Always try and look at a whole graph for the full picture. There is a media bias of 'balanced' reporting. Argument to moderation (also known as middle ground, false compromise, gray fallacy and the golden mean fallacy) is a logical fallacy which asserts that a compromise between two positions is correct. On that basis, the media give undue weight to the opinions of climate sceptics. As another example of the effect of the fallacy, the MMR vaccine doesn't cause autism, but many people still think that there is a slight risk, because they imagine that there must be some truth in the original paper. One major difficulty with realising the threat is that the most important cause, carbon dioxide, can't be seen, smelled or touched. One way of persuading people that anthropogenic climate chnage is possible is to remind them just how thin the atmosphere is relative to the size of the earth.
We need to utilise human nature. The virtuous are virtuous for no other reason than that it enables them to join forces with others who are virtuous, to mutual benefit: universal benevolence evaporates on the stove of human nature. Humans cooperate via competition, conformism helps cooperation and information cascades. The trick is to make climate change fashionable. BP and Shell have both become more environmentally friendly. There is hope, the problem of ozone depletion was tackled and is considered a success story. I used to wonder if the sea level would really rise, because as Archimedes discovered, when floating ice melts, the water level remains the same. However, global warming will cause the water level to rise because 98% of the world's ice is grounded, and in the Antarctica floating fresh water ice melting in sea water will cause the level to rise. Even if climate change has not been anthropogenic so far (which it has), all that is required is that 1) we need to change the climate, 2) we can change the climate. The major problem the earth faces is population growth, so perhaps we should legislate not per head, but per unit area. There are three potential goals: stabilize emissions, stabilize concentrations or stabilize temperature.
First, we must decide how best to deal with uncertainty. A Dutch book is a gambling term for a set of odds and bets which guarantees a profit, regardless of the outcome of the gamble. At the very least, one who practices self-consistent reasoning should not be susceptible to having a Dutch book made against them. If an individual is not susceptible to a Dutch book, their previsions are said to be coherent. A set of betting quotients is coherent if (Ramsey 1926; de Finetti 1937; Shimony 1955) and only if (Kemeny 1955; Lehman 1955) they satisfy the axioms of probability. On this basis, it is my view that probability is both necessary and sufficient when dealing with uncertainty.
Expected utility theory (also called von-Neumann Morgenstern utility) (Bernoulli 1738; von Neumann and Morgenstern 1944; Bernoulli 1954) states that when making decisions under risk people choose the option with the highest utility.
The second-most cited paper ever to appear in Econometrica, the prestigious academic journal of economics, was written by the two psychologists Kahneman and Tversky (1979). They present a critique of expected utility theory as a descriptive model of decision making under risk and develop an alternative model, which they call prospect theory. Expected utility theory is unable to explain why people are often simultaneously attracted to both insurance and gambling. Kahneman and Tversky found empirically that people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty; also that people generally discard components that are shared by all prospects under consideration. Under prospect theory, value is assigned to gains and losses rather than to nal assets; also probabilities are replaced by decision weights. The value function is defined on deviations from a reference point and is normally concave for gains (implying risk aversion), commonly convex for losses (risk seeking) and is generally steeper for losses than for gains (loss aversion). Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities. Tversky and Kahneman (1992) superseded their original implementation of prospect theory with cumulative prospect theory. The new methodology employs cumulative rather than separable decision weights, applies to uncertain as well as to risky prospects with any number of outcomes and it allows different weighting functions for gains and for losses. The theory--which they confirmed by experiment--predicts a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability.
Policy decisions ultimately require ordinality, so probability distributions should be mapped to certainty equivalent. But how? It is my contention that we use a normative model from economics--expected utility theory--and a descriptive model from psychology--prospect theory--to formulate a rational but realistic compromise between the two: a prescriptive model of risk preferences.