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What is an Infinite Risk?

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Infinite risk is a potential for an event or ongoing problem that has infinite impact.
As an example, the loss of our only known habitable planet due to factors such as an environment problem or war can arguably be considered an infinite impact. This can be modeled with two scenarios: one in which humans don't last forever due to loss of our habitat and one in which we somehow manage to survive to infinity.
Infinite risks have an interesting mathematical property in that they aren't affected much by probability. In fact, any non-zero probability of an infinite risk results in a probable loss of infinity no matter how small the probability becomes.
Risk = 0.1 × ∞ = ∞
Risk = 0.01 × ∞ = ∞
Risk = 0.000001 × ∞ = ∞
Risk = 0.00000000001 × ∞ = ∞
This means that infinite risks represent a large threat even if they have a very low probability of occurring. It can be demonstrated that reducing the probability of an infinite risk to zero, always has a return on investment of ∞, as long as your costs are less than ∞. For example, if you spend $1,000,000,000,000 to eliminate an infinite risk with a 0.00000001 chance of occurring your return on investment is ∞.
return on investment = ((gain – cost) / cost) * 100
= (((0.00000001*∞) - 1,000,000,000,000) / 1,000,000,000,000) * 100
= ∞
The mathematical properties of infinite risk suggest that investments to eliminate an global catastrophic risk can achieve high return on investment even if the probability of that risk is extremely low.
Overview: Infinite Risk
Type
Risk
Definition
A non-zero probability of an infinite loss.
Value
Infinite risk is essentially an abstract concept, much like infinity itself, that can be used to examine the far edges of a risk distribution.
Related Concepts
Probability Impact Matrix
Logic
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