Expected value is the general notion of the average-case outcome of a random variable. In probability theory, the expected value of a random variable, E[X], is the average of its possible values weighted by their probabilities.
Expected utility is the expected value of a utility function. Since “value” is a synonym for utility, I often use “expected value” and “expected utility” interchangeably, especially when the ethics/EA context is understood.
Someone correct me if I’m wrong, but as I’ve typically framed it, “value” is just a variable (which could be utility, but could just be an input like money that does not directly/linearly translate to utility) whereas utility is directly the well-being.
Take a hyper-dramatic example, simplified for illustration:
Suppose you need to have $100 in order to pay for some kind of life-saving medicine, but you only have $50. Suppose however you can place a bet that gives you a 10% chance of doubling your money, and a 90% chance of losing it.
The expected value of the bet, in terms of money, is just $10, whereas the expected value of not betting is $50. But most people can see you should obviously take the bet because you care about expected utility, which with the bet is “10% chance I don’t die now” whereas without the bet it’s “0% chance I don’t die now.”
Excellent question!
Expected value is the general notion of the average-case outcome of a random variable. In probability theory, the expected value of a random variable, E[X], is the average of its possible values weighted by their probabilities.
Expected utility is the expected value of a utility function. Since “value” is a synonym for utility, I often use “expected value” and “expected utility” interchangeably, especially when the ethics/EA context is understood.
Someone correct me if I’m wrong, but as I’ve typically framed it, “value” is just a variable (which could be utility, but could just be an input like money that does not directly/linearly translate to utility) whereas utility is directly the well-being.
Take a hyper-dramatic example, simplified for illustration: Suppose you need to have $100 in order to pay for some kind of life-saving medicine, but you only have $50. Suppose however you can place a bet that gives you a 10% chance of doubling your money, and a 90% chance of losing it. The expected value of the bet, in terms of money, is just $10, whereas the expected value of not betting is $50. But most people can see you should obviously take the bet because you care about expected utility, which with the bet is “10% chance I don’t die now” whereas without the bet it’s “0% chance I don’t die now.”
Thanks for this. :)