I have been reading a paper by Bove & Elia (2011), where they quote a definition of the value of statistical life from Bellavance, Dionne & Lebeau (2009). I have tried making my peace with the necessity of this concept, but I have been rather confused by the used definition. It says that the value of a statistical life is a function of the willingness to pay to reduce the risk of death and the risk of death itself. However, the risk of death reduces the value of a statistical life. Why would it do that? Is it a weight as in an NPV calculation, where the risk of default reduces the expected cash flow?
If you're willing to pay \$10 to reduce your risk of death by 1 in 1M, then your VSL is \$10M.†
Example. Say there are two bike helmets. One costs \$20 while the other costs \$30. The two helmets are exactly identical, except that the more expensive one has been proven to reduce your risk of death by an additional 1 in 1M.
If you're willing to buy the more expensive helmet, then your VSL is (at least) \$10M. (If you're exactly indifferent about buying the more expensive helmet, then your VSL is exactly \$10M.)
I'm not sure what you mean by "the risk of death reduces the value of a statistical life."
†At least under the simplest approach, which ignores other important considerations like risk aversion and the discrepancy between willingness-to-pay and willingness-to-accept.