Has the "dismal theorem" practical implications? The so-called "dismal theorem" asserts that we do not appropriately account for catastrophic scenarios which have very small probability of occurrence. It has been studied in details by Martin's Weitzman, notably in his article "Additive Damages, Fat-Tailed Climate Dynamics, and Uncertain Discounting".

The articles of Martin Weitzman rely on a large dose of mathematics, and my skills do not allow me to get everything, nor of course to question the reasoning and deductions of Weitzman. His conclusion is broadly that "The take-away message here is that reasonable attempts to constrict bad-tail fatness can leave us with uncomfortably big numbers" (p19)

I would like to know if there are actually any practical implications from this dismal theorem. In particular concerning climate change. I thought so until @Dole pointed out that the dismal theorem could also be used to justify trillions of dollars in investment in a anti-asteroid defense system. I would appreciate any insight on the conditions to apply this theorem, if it can ever be used. Any relevant literature would also help me.
My conclusion based on reading his paper is that the utility function of an individual or society can't be of the CRRA form presented in the paper. That would indeed lead to scenarios where you could not get out of the bed in the morning, as minimizing the tiniest probability of an enormous risk would warrant infinite sum of money.

I will attempt to explain the mathematics of the paper. First the utility as a function of consumption is of the form:

$$ U(c) = -c^{1-a}, \space a&gt;1$$

This is also called a constant relative risk aversion utility function. Constant relative risk aversion with regards to consumption means that a person prefers a bundle of 1 utils over uncertain bundles with expected value of 1 utils. The same applies to 2 utils to the same degree proportionally. Note that the utility is $-\infty$ when consumption reaches 0. 

Now, if you want to calculate the exact utility that a person receives you simply multiply the probability of each bundle with the utility it grants:

$$P_1*U(C_1)+P_2*U(C_2)... = \sum_{n=1}^{\ b}P_n U(C_n)$$

Where P denotes a probability of a given bundle and U(c) is the utility.

Finally, consider a case where there is a possibility of a bundle that has consumption value of 0, with probability greater than zero:

$$ P_x U(c_x) = -\infty $$

It does not matter what the probabilities and utilities of other bundles are as you can't recover from minus infinite utility.

The same principle applies to continuous probability distributions, so just replace the sum sign with an integral and consider case where it doesn't reach 0 probability when c=0.

You may be interested in readin Nordhaus's response:
http://aida.wss.yale.edu/~nordhaus/homepage/documents/weitz_011609.pdf (By the way, he uses the exact same case scenario as I did).