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so on. The sum of the cares is 1 + 1 2 + ( 1 2 ) 2 + ( 1 2 ) 3 + · · · = 2. In this world,
we weigh our children and all their descendants about equally in our
concerns. We might use different generational discount weights, but we
can deal with the problems as long as there is some discounting of the
future.
Now take the example of zero discounting, which is sometimes ad-
vocated by philosophers. In this family example, suppose that we have
no anxiety discounting for future generations, so we are just as anxious
about our grandchildren as about our children, and about our great-
great-great-grandchildren as our grandchildren. To use our numerical
example, the sum of undiscounted anxieties would be infi nite (i.e.,
equal to 1 + 1 + 1 + · · · = ∞). In this situation, most of us would dissolve
in a sea of anxiety about all the things that could go wrong for distant
generations from asteroids, wars, out-of-control robots, fat tails, smart
dust, and other disasters. We would simply be unable to decide what to
do. Zero discounting is like an infi nitely heavy load on our shoulders.
This argument sounds like a bit of fl aky pseudo-mathematics, but it is
exactly the nub of the deep mathematical analysis of zero discounting
made by Nobel Prize-winning economist Tjalling Koopmans. 9
So here is the short summary. We need to use a discount rate that re-
fl ects the actual market opportunities that societies face, not an abstract
defi nition of equity taken out of the context of market realities. The
logic of market discounting is not just a selfi sh view that the future
should take care of itself. It does not hold that we should consume all
our income and make no investments to protect our world or future
generations. Nor does it hold that we should ignore impacts a few decades
in the future. Rather, it refl ects the fact that there are many high-yield
investments that would improve the quality of life for future genera-
tions. The discount rate should be set so that our investable funds are
devoted to the most productive uses. A portfolio of effi cient investments
would defi nitely include ones to slow global warming. But it also in-
cludes investments in other priority areas—health systems at home,
cures for tropical diseases, education around the world, and basic re-
search on all kinds of new technologies.
 
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