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A second polar case involves uncertainties about where the tipping
points occur, which leads to a quite different outcome of acting in a
highly risk-averse manner. In the polar case, we would adopt a more risk-
avoiding path in the spirit of the precautionary principle. This principle is
used in many different areas. In 1992, the United Nations' Rio Declara-
tion on Environment and Development stated, “Where there are threats
of serious or irreversible damage, lack of full scientifi c certainty shall not be
used as a reason for postponing cost-effective measures to prevent envi-
ronmental degradation.” 7 A more radical statement is that in the absence
of scientifi c certainty, society should make policies that would prevent the
worst outcome (a “minimax” strategy in game theory).
Without adopting a particular doctrine here, we can use our cost-
benefi t approach to determine what the optimal policy would be with
uncertain tipping points. Begin with limited participation and discount-
ing. Then assume that scientists have discovered a sharp tipping point.
It might be some runaway greenhouse effect or a rapid disintegration of
the giant ice sheets. If we ignore uncertainty, the cost-benefi t analysis
would look like Figure 32.
But suppose that further analysis reveals uncertainty about the
temperature at which the tipping point enters. Perhaps there are two
equally likely outcomes in which the tipping point might be either 3°C
or 4°C. So we should really draw two different damage curves, one
turning up sharply at 3°C and the other turning up at 4°C. We would
then give each of these a weight of one-half (because that is the proba-
bility of each) and make this the new damage curve. We now have a
super-strange W-shaped damage curve.
If we go through this exercise, we fi nd that the lower temperature
threshold dominates and drives our policies. We should aim for policies
that are around 3°C even though the expected value of the tipping
point is 3 1 2 °C. The reason is intuitive. If there are multiple catastrophic
outcomes, we want to avoid all of them if we can afford to. So we take
policies to avoid the fi rst catastrophic threshold we are likely to en-
counter, which in this case is the 3°C threshold.
While this example supports the minimax version of the precau-
tionary principle, it rests on extreme assumptions. Using a minimax
 
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