“Let’s say you’re dying of thirst, you only have $1.00, and you have to choose between a vending machine that dispenses a drink with certainty for $0.90, versus spending $0.75 on a vending machine that dispenses a drink with 99% probability. Here, the 1% chance of dying is worth more to you than $0.15, so you would pay the extra fifteen cents. You would also pay the extra fifteen cents if the two vending machines dispensed drinks with 75% probability and 74% probability respectively. The 1% probability is worth the same amount whether or not it’s the last increment towards certainty.”
OK, the benefit of a 1% chance of surviving with $0.10 in my pocket is the same regardless of whether I move from 99% to 100% or from 74% to 75%. However, the costs differ: in the first case I lose (U($0.25)-U($0.10))0.99, while for the second I lose (U($0.25)-U($0.10))0.74.
“Let’s say you’re dying of thirst, you only have $1.00, and you have to choose between a vending machine that dispenses a drink with certainty for $0.90, versus spending $0.75 on a vending machine that dispenses a drink with 99% probability. Here, the 1% chance of dying is worth more to you than $0.15, so you would pay the extra fifteen cents. You would also pay the extra fifteen cents if the two vending machines dispensed drinks with 75% probability and 74% probability respectively. The 1% probability is worth the same amount whether or not it’s the last increment towards certainty.”
OK, the benefit of a 1% chance of surviving with $0.10 in my pocket is the same regardless of whether I move from 99% to 100% or from 74% to 75%. However, the costs differ: in the first case I lose (U($0.25)-U($0.10))0.99, while for the second I lose (U($0.25)-U($0.10))0.74.
I also noticed that and was wondering how many comments it would take before somebody nitpicks this fairly trivial point.
It was 6 ;)