utility elicitation is the process to go from Rational Preferences to a utility function. **Its a bad idea to use money to do this, because money is not linear.**

Consider the best and worst possible events:

\begin{equation} \overline{S}, \underline{S} \end{equation}

We assign the best event to have utility \(1\), and worst to have utility \(0\):

\begin{equation} \begin{cases} U(\overline{S}) = 1 \\ U(\underline{S}) = 0 \end{cases} \end{equation}

Given some test event now \(S\), we try to find the \(p\) such that we can set up a lottery:

\begin{equation} S \sim [\overline{S}:p; \underline{S}:(1-p)] \end{equation}

because the desirability of \(S\) is between the best and worst possible events, the continuity von Neumann and Morgenstern Axiom states that this \(p\) exists.

Once this \(p\) has been figured, we then assign:

\begin{equation} U(S) = p \end{equation}