In this chapter we return to general decision under uncertainty, with event-contingent prospects. As in Chapter 1, we assume that prospects map events to outcomes, as in E1x1 … Enxn. Superscripts should again be distinguished from powers. EU is linear in probability and utility and, hence, if one of these is known – as was the case in the preceding chapters – then EU analyses are relatively easy. They can then exploit the linearity with respect to the addition of outcome utilities or with respect to the mixing of probabilities. Then the modeling of preferences amounts to solving linear (in)equalities. It was, accordingly, not very difficult to measure probabilities in Chapter 1 and to derive the behavioral foundation there, or to measure utility in Chapter 2 and to derive the behavioral foundation there.

In this chapter, we assume that neither probabilities nor utilities are known. In such cases, results are more difficult to obtain because we can no longer use linear analysis, and we have to solve nonlinear (in)equalities. We now face different parameters and these parameters can interact. This will be the case in all models studied in the rest of this book. This chapter introduces a tradeoff tool for analyzing such cases. This tool was recommended by Pfanzagl (1968 Remark 9.4.5). Roughly speaking, it represents the influence that you have in a decision situation given a move of nature.