 Exactly how much is gaining $19 worth to you? What is \(u(+$19)=\ldots\), exactly? We can actually answer this question if we just set a scale first. For example, suppose we want to know exactly how much you value a gain of $19 on a scale that ranges from gaining nothing to gaining $100. Then we set \(u(+$0)=0\) and \(u(+$100)=1\), so that our scale ranges from 0 to 1. Then we can calculate \(u(+$19)\) by asking how much you would be willing to risk to gain $100 instead of just $19. That is, suppose you had a choice between just being handed $19 with no strings attached vs. being offered a (free) gamble that pays $100 if you win, but nothing otherwise. How high would the probability of winning that $100 have to be for you to take a chance on it instead of the guaranteed $19? Given what’s at stake—making it home for the night vs. sleeping rough—you probably wouldn’t accept much risk for the chance at the full $100 instead of the guaranteed $19. Let’s say you’d accept at most .01 risk, i.e., the chance of winning the full $100 would have to be at least .99 for you to trade the guaranteed $19 for the chance at the full $100. Well, then, on a scale from gaining $0 to gaining $100, you value gaining $19 quite highly: .99 out of 1. (This method of measuring utility was discovered and popularized by von Neumann and Morgenstern (1944), though essentially the same idea was previously discovered by Ramsey (1964 [1926]).)